Did the episode even say his name? If not the only way someone would think it was a parody of someone in particular would be to recognize someone acted like that.
My thought would be, John Doe doesn't act like that, so it must not be them. And whoever I thought did act like that, well.. it's not much of parody then. Just a shoe that fit. If it is okay to act like that, then why take it down? If it isn't okay to act like that, why would a person acting like that not have been reguarded as bad.