Let's say Person A often says certain sorts of things, which, to Person B, sound like personal attacks. Person B is offended and infuriated and begins a vendetta against Person A. Person A says, I'm sorry you took it that way; I didn't mean it like that. Person B has two choices: go around the wiki proclaiming that Person A is uncivil, never assumes good faith, and is racist; or forgive, forget, move on.
In that example, person B has apologised (for the misunderstanding, rather than for doing something wrong, but it'll do), so the dispute should be resolved at that point. If Person A isn't willing to accept the apology, then they clearly just want to cause trouble, so telling them to move on isn't likely to help.