This is precisely why it's important that Twitter calls out when things are stated as fact without evidence. Twitter never actually say things are fake; they say things are baseless and without evidence. If you want to post things that are influential you simply need to back that claim up with something that people can verify from a trustworthy source - 'fake news' will still be posted because sometimes even a trusted source gets it wrong, but it'll happen far less often. That's the goal.
Suggesting that we should all adopt Nietzsche's perspectivist approach where "there are no facts, only interpretations" is entirely unhelpful. You can't run a functioning society if you have to accept literally every batshit mental theory as "well it might be right, we can't ever know for sure". If there is no evidence, you can say something is fake. You just have to accept that maybe 0.1% of the time you'll be wrong.
