I totally understand your standpoint and I will dive deeper with your provided link but as I said before for the general public a true statement is indeed a fact.
I believe you have it in reverse. "fact" checking is there to show a minority of people that the information they are about to consume is against what is believed to be true by the scientific community and the public at this point in time.
In regards of "fact" checking this is where we at right now. That's also why I wrote not only in public but also in the scientific community, but you are right, maybe it is a Galileo situation.