I think it depends how genuine the apology is. If it's just "can we put it in the past and move on?" or if it's "I really messed up and I'm sorry beyond words and I don't ever want to do that again... can we put it in the past and move on?" it makes a big difference to me.

Asking me to forget something that you haven't acknowledged was a big balls up makes it hard to trust it wont happen again and I'll also have a wall up with that person. If they're really sorry then I can accept that because none of us are perfect and we all make mistakes so I could forgive then.