“Truth” and “fact” have as many definitions as “is” for the left. Something can be “fake but accurate” and still a “true” “fact”. Something can be decided in court settlements to have happened but still be “untrue” (e.g. “Bill sexually assaulting women”)
No reason to debate the accuracy of “fact-checkers” until there is an agreement on the word “fact”. Most of the “fact-checkers” come from the Dan Rather School of Journalism where the motto is “Fake But Accurate”. So you need to give up the “old and outdated” definition of “fact” to enter the debate on “fact-checking”.
The most absurd category of fact checking is when a statement about the future. How is it possible to fact check a statement about the future.
A candidate says the country will be X in 5 years if we don’t change course. I will do Y if I am elected.
That Fact checkers then rate those statements proves that the fact checkers are frauds. Find fact checkers who stick to statements about the past and I’ll respect them just for that.