NBC reported this
When pressed later by a reporter if his ideas were dangerous, Trump turned to Birx and asked her if she'd ever heard of light and heat treatments. "Not as a treatment," Birx responded.
That didn't touch disinfectants (alas), but clearly Birx thought that was a question worth answering. She didn't say "he was joking".
In a clip from the interview with Jesse Watters, which is set to air Saturday night, Birx said Trump was given new information shortly before the briefing, and he likes to "talk that through out loud and really have that dialogue."
"He was still digesting" the information, Birx said
In the Fox News piece alluded to an anchor says (1:20) Trump was "spitballing". So clearly somewhat more favorable interpretation(s), but not quite giving him a pass as "sarcasm". Some of the other Fox News panelists went after the (left-wing) media as implying Trump could have seriously suggested something like that; their main counter being that it doesn't matter if Trump said it, because it's so preposterous nobody would believe it. YMMV. Immediately after that another panelist says (4:30) that public health agencies have been "inundated" with calls about it, but dissed it as "who knows?"
The Intercept (which is hardly favorable to Trump) posted this narrative/explanation of whom was saying what to whom:
Apparently recounting a conversation with Bryan just prior to the briefing, Trump said that he had asked the science advisor if those techniques work so well to clear the virus from nonporous surfaces, like doorhandles or metal swing sets, why not try them on humans?
“So I asked Bill a question,” Trump told reporters as Bryan took a seat beside Birx. “‘Supposing we hit the body with a tremendous– whether it’s ultra-violet or just very powerful light?'” Trump said. “And, I think you said,” the president continued, turning to Bryan, “that hasn’t been checked, and you’re going to test it.”
“And then I said,” the president went on, “‘Supposing you brought the light inside the body, either through the skin, or some other way?’ And I think you said you’re going to test that too. Sounds interesting.”
“We’ll get it to the right folks who could,” Bryan replied.
“Right,” Trump said. “And then I see the disinfectant, where it knocks it out in a minute, one minute. Is there a way where we can do something like that, by injection?” Trump asked. It was at this point that Birx, who had been looking up at the president from her seat offstage, dropped her gaze.
“Almost a cleaning,” Trump went on, describing his proposed therapy for Covid-19 patients. “So it would be interesting to check that,” Trump said to Bryan. “So that, you’re going to have to use medical doctors with,” he added. “But it sounds, it sounds interesting to me. So we’ll see, but the whole concept of the light, the way it kills it in one minute, that’s pretty powerful.”
In the second half of Thursday’s briefing, Bryan had been forced to clarify to reporters that his lab had never suggested injecting cleaning products into humans and had looked at the effect of sunlight on the virus on nonporous surfaces, not people — not even what Trump described as the “sort of semi-nonporous surface” of a person’s hand.
As far as I can tell from short clip posted, Bryan said "we don't do that in our lab[s]" in response the question "there is no scenario in which that can be injected into a person, is there?". But again Bryan (too) took the question seriously.
And the Intercept article also mentioned this CDC report (as to show this matter shouldn't be taken lightly):
During January–March 2020, poison centers received 45,550 exposure calls related to cleaners (28,158) and disinfectants (17,392), representing overall increases of 20.4% and 16.4% from January–March 2019 (37,822) and January–March 2018 (39,122), respectively. Although NPDS data do not provide information showing a definite link between exposures and COVID-19 cleaning efforts, there appears to be a clear temporal association with increased use of these products.
And USA Today related/linked the same (later) exchange with Bryan as:
"And then I saw the disinfectant, where it knocks it out in one minute, and is there a way we could do something like that by injection inside or almost a cleaning," the president said during his White House press briefing. "As you see it gets in the lungs, it does a tremendous number on the lungs, so it would be interesting to check that."
Afterwards, Bill Bryan, an undersecretary of science and technology at the Department of Homeland Security, clarified that that wasn't possible and said, "We don't do that within that lab, at our labs."
However, Trump replied: "maybe it works, maybe it doesn't work."
Factcheck.org transcripts that as:
ABC News chief White House correspondent Jonathan Karl, April 23: The president mentioned the idea of a cleaner, bleach and isopropyl alcohol emerging. There’s no scenario where that could be injected into a person, is there?
Bryan: No, I’m here to talk about the finds that we had in the study. We don’t do that within that lab at our labs.
Trump: It wouldn’t be through injection. We’re talking about through almost a cleaning, sterilization of an area. Maybe it works, maybe it doesn’t work. But it certainly has a big effect if it’s on a stationary object.
But I honestly cannot tell who said "It wouldn’t be through injection." from the video myself. The voice saying that seems to me to be closer to the reporter's so perhaps he interjected again. Trump's voice is (much more) clearly heard saying the part starting at "We're talking [...]".
Regarding Trump's later claim of sarcasm, Factcheck.org says:
Again, we didn’t detect any sarcasm – and we aren’t alone in that – but since sarcasm is subjective, we’ll leave it to readers to make up their own minds about the president’s intent.
And from the latter link, more Fox News dismissal of the idea that Trump was being sarcastic:
Fox News’ Bret Baier isn’t convinced by President Donald Trump’s Friday claim that he was being sarcastic when he suggested ingesting or injecting disinfectants to treat COVID-19. [...]
“What’s problematic for this president is that sometimes he goes on these riffs and when you’re dealing with medical things, statements — when you are riffing from a podium — sometimes that works great on other topics when politics comes into play,” Baier continued. “But when riffing about possible cures or treatments, it didn’t seem like it was coming off as sarcastic when he was talking and turning to Dr. Birx on the side.”
Fox Business Network’s Neil Cavuto, too, hit Trump on his own show Friday, saying, “From a lot of medical people with whom I chat, that was a dangerous, crossing-the-line kind of signal that worried them because people could die as a result. Now, he might have said he was sarcastic and flippant and making the comment; I quoted directly from his full remarks. Nothing was taken out of context. I am not part of some fake news media or what-have-you. I want to be very very clear on that. Whether it cuts to the left or the right, I am not here to carry any party’s political water. I am here to help you folks out with what is real and what progress is being made, what is a legitimate issue and what is not. That’s to take nothing away from the president’s health care task force and doing yeoman’s work in trying to get this thing under control, but saying remarks like that really don’t help the matter any.”
So "riffing from a podium" instead of "spitballing" is the description in another Fox News segment, but generally it seems even on Fox News Trump's defense of sarcasm didn't go well. (The other description from Fox Business was even less charitable: "dangerous, crossing-the-line kind of signal" albeit attributed to "medical people with whom I chat".)
CNN has now posted a side-by-side camera footage from Trump and Birx and also of some of the follow-up questions (but alas not during Bryan's). But from this extra article/footage, a part I've missed in the previous articles about this is when Trump says "I'm not a doctor, but I have a good you know what" (pointing to his head) and "I'm here to present talent, to present ideas." CNN's own article [text] explains that Trump may have had less time to prepare for this briefing than for others (which may explain him "riffing/spitballing" in public, during the press conference):
When Bryan arrived Thursday with a camera-ready presentation, Trump again wasn't at the 3 p.m. ET coronavirus task force meeting, the sources said. But in the minutes before Trump's planned early evening news conference, Bryan quickly explained his findings to the President in the Oval Office.
Moments later, Bryan was standing at the White House podium explaining how sunlight, ultraviolet rays and disinfectants -- such as bleach and alcohol -- could shorten the half-life of coronavirus.
But when Bryan's explanation ended, things went sideways. As his health advisers looked on expressionless, the President started lobbing questions about whether light or disinfectants could be used inside the human body to cure coronavirus.
And yeah, the WH seems to have changed habits in the aftermath:
At Friday's briefing -- at 22 minutes, the shortest since Pence got involved with the task force -- the President walked off without taking any questions.
For a bit more background on the level of involvement of Trump in the internal briefings (thus his level of preparedness) CNN says:
While he almost always attends the daily press briefings, Trump rarely attends the coronavirus task force meetings that precede them. The task force doesn't seem to mind.
According to one person close to the task force, the meetings become more prolonged if Trump attends and often go off script. When Pence is at the helm, aides say, they usually tick through the agenda rapidly. Trump comes to roughly one briefing a week. At times, 10 days or more have passed without him attending.
So yeah, you could say that it was a PR disaster fairly likely to happen in that perspective.
More often than not, however, senior members of the task force brief Trump in the Oval Office after their formal meeting in the Situation Room -- as they did this week, when the official from the Department of Homeland Security offered Trump a presentation on the effect of sunlight and disinfectant on the virus.
Trump seemed enthusiastic about the presentation and asked the official, Bryan, to deliver it again to reporters during the daily early evening press conference. But Trump did not let on that he would raise the idea of using light and disinfectant as treatments while he was in front of the cameras, a move that took many aides by surprise. Some aides, like Meadows and newly installed press secretary Kayleigh McEnany, voiced concern that Bryan's presentation had not been thoroughly vetted and was prematurely presented to the President, three people familiar with what happened later said.
The medical musings the country witnessed on Thursday were familiar to members of the task force, however, who have listened silently as Trump raises various medical theories with little basis in science or fact.
Some members of the task force, including Dr. Anthony Fauci, are outspoken in debunking some of Trump's claims, including on unproven treatments.
But others on the panel, such as Birx, have adopted a different approach. Aides describe her as patient in meetings with the President, even when he is offering his lengthy medical opinions or theories. Instead of interjecting or cutting him off, she has waited for him to finish before laying out more reality-based ideas.
So according to that CNN article, the only unusual event here was that Trump let out his [medical] "riffing/spitballing" in public (at the press conference) on that occasion.