It has to do with belittlement: an audience's feeling of being dissed, and its desire to see the culprit shrink. The problem is, big stars don't want to become little planets.

So how does a bigshot--or you, for that matter--apologize without shrinking? Follow these steps:

Own up to the mistake. Tell the truth, the whole truth, and nothing but the truth.
Focus on your emotions, not how you hurt someone else. Say how bad you feel about screwing up.
Show how your mistake was an exception to the rule. You're a great, thoughtful person who temporarily lapsed.
Promise improvement and show what you're going to do to fix any remaining problems.

Here's a video I did with details.