Whenever a discussion about overuse of the word "sorry" comes up, I automatically think of a something my math teacher once told me.
I was writing a test. And, just like any other test I'd ever written, I was the last one finishing up. Half an hour after class ended. I obviously felt bad, making him wait so long, just so I'd be able to finish. So naturally, I apologized. He replied with something like, "you're not sorry. You'll do it again next time." So I said something like "maybe. I'm just so slow. But I do feel really bad." Which is when he told me, "you're not sorry though, you just feel badly about it."
Since then, I almost think that when someone apologizes. If they had the chance, would they change it? Or would they do the same thing over again? To me, that's what deprecates actually feeling sorry, and simply feeling bad.