It's a good question.
I guess one part of it is that alt-right sources pre-inoculate readers against potential sources of truth, by calling them liars.
For instance, Snopes is often held up as a good place to go to debunk things. Except one of the things you learn early on from even moderate right-wing sources is that Snopes is apparently massively left-wing-biased, and since they've been wrong or biased on a couple of things, it means their entire worldview is suspect. And of course you can't trust any of the lying mainstream media.
So at that point you hit up Google and - surprise - the only sources of truth remaining are right-wing sites, and left-wing blogs trying to discredit them; but the left-wing blogs have a very obvious political bias, and they're just written by some guy in a basement, so of course they're lying too. So you're left with only writing that confirms what you suspected in the first place.
I guess the only way out of that is to be smart enough to notice the internal inconsistencies or plot holes, or that some of the facts that are being asserted simply cannot be true - and then principled enough to care about that. Both of those are probably quite high hurdles for a casual news-reader.
Certainly in less extreme circumstances, when I have occasionally checked moderate right-wing sites to fact-check my own left-wing news sources, I have found it very hard to trust that those sites might be correct, and that my favourite news site might be mistaken. And I don't do that anywhere near as often as I should do.