>> So, I think it is a perfectly valid apology if basically the only thing you regretted about your actions was that it made someone upset > This is what makes it a non-apology. reply

This issue is one that my views have changed on over the years, and I've spent some time thinking about it. I currently do sometimes give that "non-apology", if you will. What else do I say when A) someone was hurt by something I said, but B) I don't know what I should have said differently? I genuinely feel bad for someone who is hurt by my actions, even if I feel that I couldn't have predicted/avoided it.

It's kind of like when two people start talking at once--there's no real fault there; you can apologize without feeling "man, I really should have not started talking", assuming there were no cues.