The lower trust in their own media might have something to do with how blatantly dishonest those sources are. But it also likely means that their viewers have lowered any standards they might have ever had. They aren't going to be shocked if they see the lies exposed, they can just shrug and say that everyone lies but the other side lies more.

Obvious falsehoods are dismissed as hyperbole, close enough to the truth that it doesn't matter if it's not entirely accurate. Omissions are just distractions cooked up by the other side to keep us from talking about the real issues. There's no expectation that reporting should be factual and follow journalistic standards, the only measure of the quality of the news source is how much they agree with it. They've been inoculated against reality.