TBH I think the answer is really quite simple and also fairly nihilistic: It's incredibly unlikely that you will personally be able to find the full truth in anything, even wildly important things like the justification of a war.
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.