We have tried teaching people not to believe everything they read on the internet already. We need solutions that actually work.

It's wishful thinking at best to believe that Twitter replies can effectively refute arguments. They don't establish public dialog unless the OP retweets the responses. You can't call it a dialogue if, effectively, there's only one person talking. Even simple refutations fail on Twitter.

"We can't fact check one person because it'd be hard to do the same for a large number of people" is classic perfect-as-enemy-of-good. We get huge bang-for-buck by handling some obvious outliers and known bad actors, and that's worth doing.