Can you specify a bureaucratic regime for distinguishing the two that you'd trust an opposition government to operate? If not, they are equivalent for public policy purposes.

To Trump supporters, The New York Times is an institution that spreads lies with abandon, and they get to operate enforcement agencies at the moment. The belief that it's seeking the truth in good faith is essentially just liberalism. Same for Fox and friends.

The best line of defense against this nonsense is education, free and of a very high quality. Absent that people will be pretty easy to manipulate. So whenever you're faced with a problem like this I would argue for better education rather than for some kind of control over the media, the liars should die out because nobody believes them anymore.

Given how incredibly entrenched some power structures based on lies are it looks as if my plan is mostly failing. Education budgets are being cut left right and center and the quality of education has been steadily trending down since ~1950 or so.

Education is locally controlled and political polarization is geographical. Right and left wing communities could both operate stellar schools and their graduates could be even less able to agree on truth.