I disagree. What of the key things you have to understand is that once fact checkers get even one story wrong, they lose credibility. After all, a fact checker supposed to be the last line of defense of truth, and when it fails, it means there needs to be a fact checker for the fact checker. Otherwise, how do we know that the fact checkers are *ever* right?
And yes, as it turns out, fact checkers are wrong at times, particularly in regard to socio-political stories. Notably, the things they're wrong about often, if not always, benefit the left side of the political spectrum. Is this surprising? No, it's not.
As for bias, fact checkers can reveal bias not only by incorrectly labeling as false things that are true, but also in what they choose - or not - to fact check.
But at the end of the day, the true threat of these fact checkers is that their errors can lead to the the censorship of people. In other words, people can be censored for expressing truth. Do you want to live in a society in which people are punished for telling the truth?