It has less to do with an ABILITY of self reflection than with a POSTURE to take in context. Look around you, you'll most probably meet many people who are ABLE to think "critically" yet fall for fake news and hoaxes. Also, there's the fact that it's easier to detect false information on questions you are familiar with.
That's so important.
The old "modern" news has _long_ assumed a local minimum of giving the remaining audience strong opinions on things they have not personally checked. Distilled; it's a final pointless outburst of pretend-informed righteousness.
If I'm waiting somewhere watching the network that shall not be named it's an odd mix of funny and terrifying; the stuff they implicitly assume their readers do not know is so trivial... at some point you must assume it's not an accident that they also pretend not to know the unmentioned basic info.
I could link a wall of specifics, but why? Most people don't respond to being told they are wrong (myself in 04' included).
Deliberately tangential example: https://www.youtube.com/watch?v=7R3BN4T6XMw
And while you're giving some fairly radical examples, this applies to very simple and practical issues. Without stirring the hornet's nest with precise examples, it's safe to say that the reporting on most of any political issue is rarely even remotely impartial. So what is true and what is not? What we tend to believe, one way or the other, is what we want to believe - and you can certainly find some source or another stating it's true. Pair that with social media where people surround themselves with people who all mostly think the same way, and thus share a constant slew of sources all saying what these people collectively want to hear, and it leads sort of parallel realities where two large groups of people might see the color green, but one collectively convinces themselves it's blue, and the other that it's red.