Thruth isn't something variable or something that could differ from person to person. Truth is defined usually by something that's provable, usually backed up by established facts.
When people say "something could be true for someone but not for someone else", they are mixing "truths" with "beliefs". Truth doesn't have to be believed in. It is a truth, plain and simple. Your point of view doesn't matter. It's a truth.
The problem with fake news is that many outlets these days are publishing stories trying to pass them as legitimate news, but are instead either an opinion piece, or something based on rumors or informations that can't be verified.
I agree that the world is not a binary entity. It is not merely 0s or 1s. There's a whole spectrum of variables to take into account. And I also agree that people SHOULD be able to separate the BS from the real stuff, but we all know that's not the case. People usually tend to "believe" as truth whatever seems to validate their pre-conceived opinions. Even they're based entirely on non-proven "facts". THIS is the heart of the problem.
An innitiative to label "fake news", "opinion pieces", "parody websites" or "unreliable sources" as such, isn't censorship. Censorship would be to prevent those from appearing on the platform, which, as far as I know, isn't what this would be about. This would merely be a label to inform people about the content they're about to click on. Recent studies have demonstrated that people in general are more enclined to believed whatever has been shared by their friends on Facebook, than stuff coming from serious and dedicated news channels. This is a huge problem.