[ghaff]

Except, under those circumstances, I'm probably not losing any sleep over the fact that I offended you. So that statement means I'm shouldering the blame at some level but it's also typically dishonest. I'm not actually sorry I offended you because I think you're being an oversensitive idiot.

[mikeash]

Then don't apologize. If you're not actually sorry, don't say you are.

Edit: it occurs to me that this hooks straight back in to the article's question. Why are most public apologies so bad? Because most of them are made by people who aren't actually sorry.

[ghaff]

Which is a reasonable approach--although it may or may not be the best one from a PR perspective.