Update:The original post in the text below the line was grossly insensitive and condescending on my part and I'm sorry I wrote it, but I did write it and it stands intact as a testimony to my stupidity, as well as an object refered to by some clear and concise comments from
BroserUK in posts below it.
Double plus (really, that's my vote) for coming up with another version of the generic
I'm sorry you're offended
Judith Martin classes these as non-apology apologies. These statements add a second insult in the form of an apology, in this case it's basically "I'm sorry you're so immature."
In practice, these replies are a bad move, leading to further miscommunication. The insultee feels further insulted (quite reasonably), and the insultor thinks "What's the matter with him? I apologized, didn't I.", and leaves with either a vague uneasiness, or a naive self-righteousness.
Of such things are family splits and community divisions made.