Well, it's a judgment call. Is this critic operating in good faith, or not? The reporter is not necessarily in the best position to judge. On the other hand, they have the best grasp of all the details of the interaction with this (alleged) bully.

"You don't want continuing abuse" is quite different from "you don't want feedback".

Quite - I fully admit that I know nothing about that particular situation.

However, I have personally seen people get overly defensive when someone has pointed out a major error in their methodology and they have then gone on to hide their working rather than trying to fix the issue. Often it's because they are not particularly expert in that field and don't really understand the issue that needs to be fixed.

I've also seen plenty of bullies in the workplace too.