For me, an apology is coming from someone else outside me and is for their benefit, can help them better understand themselves and is part of a larger picture I create of that person for myself, starting with the initial interaction, the apology, and following. Just as they may be sincere or plastic/automatic with their apology, I can judge them positively or negatively, based on my own inner sincere/plastic/automatic perspective; they don't really have anything to do with one another.

If I misperceive, then, for me, a sincere apology might appear insincere or an insincere one might be taken as sincere. Why do those who are abused often stay with their abuser? If I am not honest with myself, my judgement can be skewed and that has nothing to do with the other person giving the apology anymore than if I am not honest with myself, I can apologize insincerely and that has nothing to do with the other person, either.