Well, that's disputed
What *I* heard was that the stories tagged as fake were actually shared a lot more - not as the article said about the tag having no effect.
When the "liberals"* call it fake, it only means it doesn't agree with their confirmation bias, and is therefore _more_ likely to be real, not less, at least in many eyes.
In my own experience, for events at which I was present, there's little correlation between what happened and what was reported in the official news. Ever. This includes my time working in the intelligence community where we had some access to data the rest of the world did not.
No relation. Or, more accurately, it's all public relations. Buy that soap! Believe your government cares about your welfare. Pay those taxes. And so on.
*liberals for example invented the idea of political correctness, regardless of actually being correct. That's not liberal - that's more restrictive - I have to think their way.
Liberals make up the majority of controlling interest at FB and in the Deep State they serve.
I promise you that exactly zero news marked as fake was pro conservative (not that conservatives are conservative anymore than liberals are liberal - both defy the dictionary). Of course, this is only obvious to those who have a brain and pay attention using an attention span longer than a goldfish.