So politely contact him on FB and say that while you don't mind fact checking per se every group he listed as helping FB has a liberal slant which has translated into anti-Republican bias.
For example snopes labeled the fact that Planned Parenthood sold baby parts for money as "mixed" by making the question whether or not one person admitted that they were "illegally" selling baby parts not that they were selling baby parts.
PolitiFact used very different standards for addressing nearly identical claims by Bernie and Trump; needless to say they were much nicer to Bernie.
Either he needs some conservative fact checkers or he needs to jettison the whole idea.
We're adults and we don't need someone else, especially biased elitist liberals, telling us what news is true and what news isn't.