There is little doubt that the cold water was deadly to many of the victims in the Titanic desaster. The figure given in the Wikipedia article, that "most people who entered the −2°C (28°F) water died in 15–30 minutes" is certainly plausible. However, note the word "most": the quote doesn't state how many lived longer than 30 minutes, but there must have been at least a few.
There is also the "rule of 50s" that has occasionally been evoked to demonstrate that there was little chance of survival for the passengers who went overboard. One popular version of this states that at a water temperature of 50°F, there is a 50 percent chance to survive for 50 minutes. While this rule appears to be something made up out of thin air in the fist place, it also doesn't say anything about the upper margin of survival. Thus, while it's certain that most passengers were dead within less than an hour after the Titanic finally sank, this doesn't mean that there might not have been a few individuals who have survived longer than that.
Indeed, there are reports of people who have survived even longer than two hours in cold water. Chances of survival seem to depend on the constitution of the individual and on their equipment. Molnar (1946) mentions a relatively spectacular case:
A corpulent man of 29, clad in indoor rig and overcoat, remained swimming for nine to fourteen hours in the sea at 30 F., while two companions died after two and one half hours of immersion. One may doubt this last case; it does not seem possible that a man, even a corpulent one, can swim for nine hours at 30 F.
Note that the author questions the more extreme part of this case, but appears to be willing to accept that the two companions survived for more than two hours. Yet, in the same article, there is another reported case where the victims were clearly less lucky:
Critchley recorded that of 10 men from a torpedoed vessel only 1 survived half an hour of immersion in sea water of 29 F. (there was a large amount of field ice about).
What becomes clear is that we have to distinguish two time estimates: the estimated time to death and the estimated survival time. Both times depend on the water temperature as well as the equipment. It is only the upper estimate – the the estimated survival time – that is of relevance here. We know that the water was cold enough to kill a person by hypothermia within much less than an hour, and no-one disputes that this happened to many of the passengers. This is what the Wikipedia quote in the question refers to, but it doesn't say anything about the much more important figure: the estimated survival time. So, what do we know about that figure?
A report by Brooks (2001) for the Canadian department of transportation summarizes findings by the Canadian Red Cross according to which the chance of survival is only slim at temperatures less than 0°C (32°F) and after an immersion duration longer than an hour:
I have found two mathematical models that have been proposed to estimate survival times, one by Hayward et al. (1975) and, more recently, Xu & Giesbrecht (2018). Hayward et al. report a series of exposure experiments to simulate accidental situations, with immersions
conducted in the sea, using persons of average build, who wore standardized, light clothing and a kapok lifejacket.
Based on the results, they estimates the survival times as
t = 15 + 7.2 / (0.0785 - 0.0034 * T),
where t is the survival time in minutes and T is the water temperature in °C (<= 23°C). For a temperature of -2°C, the estimated survival time 99.4 minutes, i.e. more than one and a half hour.
Xu & Giesbrecht (2018) use 122 cases reported in the UK National Immersion Incident Survey as the data for their study. Based on these cases, they propose an estimated surivival time of
ST = 0.0547 * T² + 0.5048 * T + 1.3604,
where ST is the survival time in hours and T is the water temperature in °C. For -2°C, their model proposes a much more pessimistic maximum survival time of 0.57 hours (~35 minutes). Yet, there is only a handful of immersions at very low temperatures (below 2.5°C), so their model may not be very accurate for the Titanic conditions.
So, given all this – is it plausible that Charles Joughin could survive being immersed in the freezing North Atlantic for a long period of time? In the official inquiry, he estimates that he survived for more than two hours:
How long do you think you were in the water before you got anything to hold on to?
- I did not attempt to get anything to hold on to until I reached a collapsible [boat], but that was daylight.
Daylight, was it?
- I do not know what time it was.
Then you were in the water for a long, long time?
- I should say over two, hours, Sir.
It's usually assumed that the Titanic finally sank at 2:20 am (local time). I couldn't find a source that stated when day broke on April 15, 1912, but using available online tools, a conservative estimate would suggest that the first daylight might have become visible at 4:20 am. This means that Joughin's estimation of the time he spent in the water is plausible. Unless he lied when he said that he was in the water for the whole time span between when he went overboard and when he reached the lifeboat, he was immersed for at least two hours.
This duration is shorter than the extreme durations reported in Molnar (1946). It's somewhat longer than the expected survival time estimated using Hayward et al. (1975), and much longer than the corresponding estimate based on Xu & Giesbrecht (2018). According to the data presented by Brooks (2001), Joughin's chances of survival were only slim.
Yet, there are a few things that may have increased Joughin's slim chances of survival. Apparently, he was never fully submerged (and hence, not fully drenched), and he was a good swimmer:
Did you feel that you were dragged under or did you keep on the top of the water?
- I do not believe my head went under the water at all. It may have been wetted, but no more.
Are you a good swimmer?
He appears to have used a fairly energy-conserving way of movement:
- Were you trying to make progress in the water, to swim, or just keeping where you were?
- I was just paddling and treading water.
And, perhaps crucially, he wore a lifebelt that helped keeping him afloat and only partially exposed to the cold water:
You had been wearing a lifebelt?
So that your feet would be in the water?
And you supported yourself by your lifebelt. I do not want to be harrowing about it, but was the water very cold?
- I felt colder in the lifeboat - after I got in the lifeboat.
So, to summarize: There is no doubt that Charles Joughin survived the Titanic incident, as he could appear in the official inquiry. If we believe the events in his testimony, he must have been in the water for two hours or more. This agrees with his own estimation. According to the publications on the topic, it is very unlikely to survive for this long when immersed in water that is as cold as -2°C, and there is no doubt that hypothermia caused the death of many of the 1500 victims on board of the Titanic (in addition to death by drowning and by physical impact).
This leaves us with two possible conclusions:
Joughin was a lucky survivor. If 1500 people perished in the water and one survived, we're at a survival rate of less than 0.001 – in other words, the water was really deadly, but one lucky person made it through it.
Joughin lied in the testimony. He was not thrown into the water at 2:20 am, and managed to get on board a lifeboat at daybreak. It is known in which lifeboat he ended up eventually (lifeboat B), but the only report of how he got there is his own testimony.
I'll apply Occam's razor and prefer the first conclusion over the second.