But fact-checking is fake news!
It'll make no difference to the deniers, because to a "man" (anthropoid, anyway), they view the very act of fact-checking as partisan. Only liberals do it, with their stupid obsession with facts and all. You say "peer review", they hear "filthy liberal fact-checkers".
I don't think they particularly want science to be on their side. These climate-change deniers are part of a tribe that thrives on martyrdom, knowing that they're despised for their beliefs, and giddy with delight when they can offend a science-loving liberal with their contempt for science.