Except that the “MSM is lying” crowd still overwhelmingly supports W. bush and the Iraq war, and didn’t seem to mind what the media had to say for 8 years of his presidency. This whole thing kicked off under Obama when “alt” news was talking about FEMA internment camps and that kind of madness, and later when Pizzagate and other stories weren’t carried in the mainstream.
If your theory were right, you’d expect the Left to be the ones who rejected the media, but that isn’t what happened.
Edit To be clear, I’m saying that this is less about skepticism (healthy) than rejection of media in favor of preferable narratives. It’s the extension of disliking what science education has to say about evolution and seeking to have Creationism taught in schools. When you can’t beat them, avoid them, craft your own narrative and reject reality.