It isn't the completely fake news that's the problem - everyone (well, 99% of everyone to be on the safe side) can see through stories such as "World War 2 bomber found on moon". But there was a recent one that Trump had narrowly beaten Clinton on the popular vote, which was nonsense, but took a bit of digging to be revealed as such - and most people won't bother.
But I'm afraid the days of fact-checking by MSM journos have long gone, They just run stories from Twitter and Facebook like everyone else, driven by click maximisation (which, in many cases is how they're remunerated).