I am fairly certain they aren't naive about setting up their fact checking organization. They want to be taken up by anyone trying to verify facts so it's not in their interest to integrate bias.

Yes, there are revisions and the fact checkers fact check the fact checkers. They aren't colluding to implement left or right bias here. They are just making matter of fact statements like "it's false that the pfizer vaccine modifies your DNA" and providing sources that verify the claim and "no, politician X did not say Y"

There's no explicit collusion, but they operate in a particular social culture and the biases of that culture will permeate everything they do. The news organisations that they're fact-checking have the same reasons to become reputable suppliers of truth; I don't see how a fact checker would end up any less biased than a newspaper, since they're ultimately subject to the same incentives.

> They want to be taken up by anyone trying to verify facts so it's not in their interest to integrate bias. Yes, there are revisions and the fact

This isn’t true. It’s easier to get business if you’re a “fact checking” organization that always fact checks in a favorable direction to a major political view.

The people who want truth is a much smaller group than the people who want their views reinforced.