This is absolutely false.
No, it's not. If they do apologize, it's usually in a fake self-serving way where it's actually a self-justification in disguise.
So, for instance, if they've said something offensive, they apologize perhaps for not realizing that the person would take offense, implying that the person overreacted due to fault of THEIRS.
Obviously you've never known anyone with narcissistic personality disorder. It's not simply arrogance or pride, but runs a lot deeper.