This frustration with fact-checkers seems genuine. Mark alluded to it in https://techcrunch.com/2024/09/11/mark-zuckerberg-says-hes-d... which squares with how the Government used fact-checkers to coerce Facebook into censoring non-egregious speech (switchboarding) https://news.ycombinator.com/item?id=41370516
Alex Stamos pushed this initiative pretty hard outside of Facebook in 2019+, seemingly because he wasn't able to do inside of Facebook back in 2016/2018. But I haven't dug into his motivations.