While there are claims that are black and white, and claims that are grey, empowering someone to enforce that clearly-false claims cannot be published is going to bite you, because that person is going to have their own perspectives, biases, and (probably) agenda. It takes something close to a saint to not inflict their own agenda, and saints are in short supply.
Umm... we have an existing legal system already does this. It certainly isn't perfect, but your argument seems to boil down to: we don't have a perfect legal system, so we shouldn't have any laws.
I don't see any reason why we can't have laws that make it illegal to run around and hand out pamphlets that deliberately misinform people about if / when they can vote.
> Roundup/glyphosate might cause some harm to someone
You seem to be using an inherently grey claim to make your point. Of course glyphosate might cause harm to someone, there is almost literally nothing that has no possibility to cause harm to someone. This is exactly the sort of claim whose truth value depends on the context and meaning with which you interpret it.
This is different from a claim like "I have a bachelor's degree from UC Davis" or "You cannot vote without a drivers license"
The point about glyphosate et al is this: Sure, those are definitely grey. But the authority could claim that they are black and white at his own discretion. If he decides against you, you then have to go to court, with the default decision being against you, in order to be able to be heard.
Are you just saying that moderation should be illegal? In what way would going to court help you if you've been moderated off a platform?
Are you attacking some sort of straw man central censorship authority that would exist outside of the courts?
While there are large grey areas in the middle where subject opinion, context, and fuzzy word definitions make truth values complicated, there are also some very clear black and white areas for blatantly false concrete claims are being made and spread that have no basis in reality. I think there are ways to regulate and pushing blatant disinformation while leaving the greyer borders up to individual discretion and discernment.