It's one of those language things. Newspeak necessarily requires co-opting the good meaning of a work in order for it to work. I am doubtful OP dislikes the true meaning of fact-checking but what "fact checking" has become in this modern age.
The problem is that there are two interpretations of "fact-checking is bad" which are not mutually exclusive:
(1) "Fact-checking" is a term used by people who are not interested in facts, but just want to control a narrative.
(2) Convincing the public that "fact-checking" is always done in bad faith is in the interest of people who do not want to actually be fact-checked, but rather want to control a narrative.
Well, that's one problem. The other problem is that (2) has the potential to be far more pernicious: it dismisses the possibility of material difference between real fact checks and propaganda disguised as such. "Fact checkers may have their own agendas" can be true without leading us to "therefore no facts should be checked." If we choose the latter, then we have largely given up on the possibility of facts at all, and we are, not to put too fine a point on it, well and truly fucked.
In the case of this BMJ article, it looks like there are reasonable questions as to whether the authors truly make a case that supports their conclusions. There's a comment from PaulDavisthe1st somewhere around here that links to both the actual article and the fact check, and it at least seems a bit more complicated than "THE BMJ IS BEING SUPPRESSED BY THE ELITES WHO DON'T WANT YOU TO KNOW THE TRUTH, MAN," which is a distinct vibe I get from the comments.
