The question is complicated.
First, we should be clear that audiologists conduct more elaborate tests than just "pure tone audiometry". Wikipedia provides a good summary, including examining the ear, and conduction more functional tests like the Words-in-Noise Test.
If we look at the hearing tests conducted by YouTube memes, Miles Kitaro tweeted an analysis of a tweet of a YouTube test:
due to video compression, the audio in this video past ~15,500 hz is absent.
(I checked Kitaro's bio, and there doesn't appear to be any relevant evidence of expertise in audio analysis, so this should be treated as "some random person on the Internet claims it.")
The next step up after a video with a fixed range is a mobile app designed specifically to test hearing.
In 2016, there was a review of the evidence, Validated Smartphone-Based Apps for Ear and Hearing Assessments: A Review.
App store search queries returned 30 apps that could be used for ear and hearing assessments, the majority of which are for performing audiometry. The literature search identified 11 eligible validity studies that examined 6 different apps.
Very few of the available apps have been validated in peer-reviewed studies. Of the apps that have been validated, further independent research is required to fully understand their accuracy at detecting ear and hearing conditions.
So, if even the dedicated apps aren't to be trusted yet, the YouTube variants should be treated with skepticism.
(To be fair, yet another peer-reviewed analysis of one smartphone app, that was dated after this review that was quite positive:
Within the adult sample, 94.4% of thresholds obtained through smartphone and conventional audiometry corresponded within 10 dB or less. There was no significant difference between smartphone (6.75-min average, SD = 1.5) and conventional audiometry test duration (6.65-min average, SD = 2.5). Within the adolescent sample, 84.7% of thresholds obtained at 0.5, 2, and 4 kHz with hearTest and conventional audiometry corresponded within ≤5 dB. At 1 kHz, 79.3% of the thresholds differed by ≤10 dB. There was a significant difference (p < 0.01) between smartphone (7.09 min, SD = 1.2) and conventional audiometry test duration (3.23 min, SD = 0.6).
They concluded that, combined with calibrated headphones, this could be used to conduct "air conduction hearing threshold" tests.
The conclusion seems to be: There is potential for relatively inexpensive equipment to be used to perform one sort of testing, but simply relying on typical equipment deployments and YouTube and Twitter's video compression algorithms cannot be relied upon.