It is not a paradox at all. Not trusting the main stream news is not the same as refusing to see what they have to say.Kind of a paradox . Some righties don't believe main news. Which by it's very definition are time tested national news organizations .
So what's the alternative? Fringe news ?! Which by definition is hyperpartisian and untrustworthy.
So where do you get your news ?
I get news from all over the place and main stream sources are included in that. I receive that news with the expectation that it is fraught with opinion and stretches the truth to the breaking point. If something is worth knowing (not the score of last nights game) then I go to other sources and corroborate it. If it is just a gee wiz that has little impact like last nights scores then corroborating is rather unnecessary.
The amount of corroboration that a story needs varies with weather or not the sources are very similar and how large the story is.
The key is recognizing that the various media outlets are NOT there to inform you or bring you the news - that is a fallacy. They are there to make money and that requires eyeballs on their articles. As such, they are going to editorialize the shit out of them to pander to their readers and (the largest problem of all) sensationalize the news pieces to the most extreme point necessary to get people tuned in.