Another problem is that something like this can function as "evidence" for the claim. There are large groups of people who believe that censorship like this validates a worldview in which powerful interests are censoring true information in order to maintain control. It's similar to the Streisand Effect or "Banned in Boston" but for belief rather than attention.

It seems like the better solution is to have an outpouring of discussion around how and why the claim is wrong. Let others ridicule the statements, rather than shutting down discussion. You'll never convince everyone, but at least you'd avoid the validation-by-censorship effect.

I could be wrong on this though. I don't really have any evidence or data that would show doing it one way is better than the other. I suppose I simply prefer open discussion.