Since "truth" is more of a philosophical concept than anything else, IMHO the problem with "fact-checking" is largely rooted in the framing of it. Instead of a

Since "truth" is more of a philosophical concept than anything else, IMHO the problem with "fact-checking" is largely rooted in the framing of it. Instead of acting like there's some objective truth that some people know for sure, it should have been framed simply as argumentation and exposition so people can follow the logic. I.e. let's say someone claims that mRNA vaccines are causing widespread heart attacks, the people who push these claims are almost always misrepresenting data through statistical tricks. Instead of just doing "fact checking" in form of "our data says it doesn't" its much more effective to address the original claim and expose the tricks used to give the impression that people are dying of heart attack after vaccination. It not only builds trust and reason but also makes people smart for understanding what's going on instead of feeling dumber than the "experts" who tell them the "truth". During the pandemic, I recall some conspiracy theorists using official data in such a way that I swear it obviously shoved that vaccinated are about to die off. I spent hours multiple times to dig out and understand what the data actually says. Every single time, it was due to some technicality like the times the data is collected or processed(data entered in batches giving the impression of people dying from something that happens periodically) or something that from a laymans meant one thing but it was actually exactly the opposite when you know it(i.e. some response from the immune systems that looks bad but actually it means that the vaccine is working as expected). Oh and my favorite, change in methodology presented as change in outcomes.