I've never heard "No one can hurt your feelings", just "no one can take advantage". I'd consider it a type of malapropism, and also a "consider the source" type of thing. But I understand the sentiment. Obviously people use words as weapons all the time, some cut deep and fast, some are like the thousand little nics that make you bleed to death.
If the person doing the insulting is making the comment, then, yes, not only are they insulting but they enjoy it. If someone else says it in response to my complaint, I would question why I go to that person for support.