You most likely would not have read about the study if that were the outcome because it would have been remained unpublished due to self-censorship or buried.

You most likely would not have read about the study if that were the outcome because it would have been remained unpublished due to self-censorship or buried. It would be an interesting experiment indeed. Getting that result isn't hard, that's just a matter of finding the right researchers to do the study just like any other study in this field (including this one). Academia being what it is is will be harder to find the 'right' candidate but that does not make it impossible. The whole concept of 'fake news' is fraught with error anyway given that it wholly depends on who gets to decide what is 'fake news'. Were and are the many claims that 'we only have X years left' fake news, especially where X has come and gone without the world succumbing to whatever was supposed to ail it? What about all those calls that 'politician Y will become a dictator' which turned out to be untrue, was that fake news? What does that say about similar calls being made about the same person at a later point in time, can those now be labelled 'fake news'? Fake news and the related 'fact checkers' are just weapons in the arsenal of the propagandists in the battle with other propagandists. In the end it is propaganda all the way down.