"Who is the arbitrator of an obvious lie[?]" Easy. The final arbitrator is the owner of the platform. It is just
one platform. If a platform becomes ban-happy, you can simply walk away, even if you weren't personally banned. Hacker News has plenty of rules and standards, and it will quickly mute and ban someone who violates even a subset of them. That is absolutely not a problem, and the platform is better off for it. It probably has a much larger userbase as a result, so the population of Hacker News users is dynamic, and HN can make decisions that benefit a lot of future users at the expense of a few current users. Why shouldn't HN be viewed negatively for that, but other platforms should? Isn't that arbitrary?
~Thought exercise~: Let's say you were the mayor of a large city. There are multiple areas in the city where you can shout whatever you want during certain hours. Would you let someone hook up an internet-connected megaphone in each area and pipe in hate speech everywhere simultaneously? And what if we were in a future where there were physical bots indistinguishable from humans that crowded into those public spaces, vociferously indicated their agreement, and cheered him on?
That future is now.
In reality, Facebook owns those public spaces. No one actually goes to that spot in the park anymore. Mark Zuckerberg is the mayor. Oh, and it's not just one city, he's everyone's mayor, everywhere. If you don't use Facebook but you're on Whatsapp, you're still in his jurisdiction. As for the "during certain hours" part? Nope, those internet-connected megaphones are blasting 24/7. Those bots are nodding their heads 24/7. Our mayor also collects megaphone usage fees for himself. He gives you dopamine points, likes, and social validation each time you come back for more. Freedom, yeah.