For what that concerns us here: LLMs will never learn to fact-check anything. They'll blindly regurgitate the facts they have been "taught", but never consider or evaluate "the paper cited for this fact on wikipedia is a bunch of bullshit".
Any attempt to use them to produce "facts" is ultimately just folly, in the same way Google's attempt to do so with it's search engine index is.
Nor do people, though! This is setting the bar way too high.
The whole point to having edited reference sources like "encyclopedias" is that so that we can rely on the expertise of the editors in lieu of having to develop the expertise ourselves[1].
No, an LLM that simply knows a priori (via prompt hacking) which sources are trustworthy would be absolutely comparable to the way an educated-but-non-expert human approaches sources.
[1] Which is a chicken and egg problem anyway. Everyone starts with edited reference sources as tutorial material. Quite frankly everyone starts learning with wikipedia.
No. If these things are claimed to be sources of truth, then the bar needs to be that high.
It is precisely because people don't fact-check that the bar has to be so high.
That's a strawman, though. No service, nor human, "claims to be a source of truth" in the kind of profound sense you seem to be using. It stops, everywhere, at "Wikipedia (or whatever) said it and I trust it".
The only way to get access to deeper expertise is to (1) BE an expert and (2) engage in an discussion with another.
GPT doesn't do math correctly but it also doesn't just memorize it.