I would prefer you not go around saying someone is "apologizing wrong" because you've found the magic formula to turn all apology text into "I'm sorry you feel bad". There's no point in making a statement like that the original person can't respond to, anyway.

I get what you're saying and I don't want that that either. But I also don't think a simple apology that doesn't attempt to justify one's actions can be so easily flipped.