One way for major "news" outlets to regain trust would be to address this head on, admit why they pushed things that they knew weren't true (or at least, had no

One way for major "news" outlets to regain trust would be to address this head on, admit why they pushed things that they knew weren't true (or at least, had no reason to believe was true), and to tell the public how and why they're going to be better. Odds of this happening is close to zero though, so this is going to be a problem. You can't keep proving the conspiracy theorists right and expect people to "trust us this time". It doesn't work that way.