Fox News spent a decade and a half systematically attempting to delegitimize the mainstream media, and now we're in a situation where nearly half the country (and more young people than I'd like to admit) genuinely distrust sources like the BBC and the Times

But foxnews is mainstream media (unless my mainstream you mean "liberal"). But it's hardly foxnews fault cause younger generation doesn't watch tv. And I doubt that it's "fake news" either, cause liberal news fb feeds like The other 98% and Occupy Democrats were equally eager to spread false and misleading content. You can't blame people for not trusting CNN which was caught helping their candidate to win debate, or MSNBC that spread unverifiable rumors about Trump. NPR is government financed and supposed to be bipartisan, but it's clearly leftist, to the point that one interview with rather polite and civil jewish breitbart editor caused it's director to suggest "these interviews should not be done live" without "contextualizing".

As for BBC, biggest their lie that I remember, was repeated claim that there are 250000 civilians trapped in Aleppo. As for right now, when Assads army captured most of rebel-help Aleppo, there is no sign of these 250k people who couldn't have disappeared from besieged area.