I disagree with this, which is why I'm so freaked out. I would have agreed with this 20-25 years ago, but not now.
For example, re: your last paragraph, I'm also from a purple district in a purple state with family equally split between the left and the right (and split into multiple factions within each). There are a lot of social incentives for people and institutions to lie and, more importantly, for the middlemen to amplify and present those lies. I also think that with so many of our fundamentals on shaky ground, a lot of the lies might not be purposeful. Scientific reporting is a good example: If the science media lauds an experiment that it turns out is non-replicatable, they're not lying on purpose but they're still reporting something that isn't true.
Scientists are incentivized to publish too often/fudge numbers/not do "boring" experiments. The NYT and Fox are incentivized to cut editors and fact checkers and reduce turn around time because people have been conditioned to expect immediate reporting. They're incentivized to cover things with a partisan slant because it goes viral.
The incentives are perverse at this point.
But like, how did you know that science media tends to do X? Scientists are incentivized to do Y? How do you know that NYT and Fox are incentivized in the ways you're talking about? The reason why they're even notable is because someone else is looking at it and going "hey!! this is going on!!" and presumably this person isn't a known liar/acting on known lies. Maybe enough independent people are saying it that collusion is statistically unlikely. But you do have a knowledge base. It's as simple as knowing what your knowledge base is, in relative to the knowledge bases others are using.
At the same time, the reason why the war justification is so notable is because it was eventually brought to light, and its unusualness of the lie made it notable enough for reporters to believe people need to hear about it.
It makes sense to me to generally conclude: liars happen, but generally dishonesty isn't something that's considered moral/ethical by society. Most people don't bald-faced lie about stuff, when they do its considered a scandal. Generally people will honestly tell some truth of what they understand from their own incomplete knowledge and that's about as good as you're going to get (there is no "objective truth").
Trustworthiness then becomes people who knowingly lie less often relative to others, or people who source their truths less often from known liars. For example, I don't believe Alex Jones on much of anything given that he's knowingly lied repeatedly, extensively, and built his career on it. But Joe Rogan I'm pretty sure just sources from liars more often than I'd like in his claims, so I don't really listen to him either. I'm more likely to believe the Slate Star Codex guy, because I don't think he knowingly lies about his analysis but he has his own biases and blindspots and so I generally don't believe what he concludes when he says things that correspond to his blindspots.