Distrusting a media source is not the same thing as being able to think critically. Lots of QANON believers distrusted the "mainstream" media (an often misused and misunderstood term), and relied instead on their own "research". They still lacked the critical thinking skills to discern truth from fiction. Most people don't know how to calibrate for priors and confirmation bias.
Get news from many sources and don't trust any one of them to get everything right, to always report accurately and fairly. It's impossible. Every article involves choices - of subject, of focus, of whom to interview, of what to emphasize and what to disregard, even of whether to report it at all. As a consumer, you have to triangulate and use hindsight to ask, "How well did the NYT or Breitbart report on that issue?"
In my experience, some news sources get most of it right most of the time. And others almost never. Trust of the mass media among Republicans is low, in part because of Trump and Fox constantly lambasting the "fake" media coupled with the dystopian notion of "alternative facts", and the cognitive dissonance that arises when "real" factual reporting contradicts preconceptions. That's hard to overcome.