I usually go out of my way to play cooperative with people. It often means that I try to say, "I wish it were possible to go back and time and restate that in a way that would achieve what I intended without hurting you".
Someone's surprising outrage at something I think is innocent also reveals my lack of understanding of that other person. Assuming their honesty, I want to go into this in order to better understand what's going on. Maybe we both actually think the same way about the issue, maybe it's just an unfortunate phrasing on my part that caused the problem? It happened this way many times.
So to circle back to the beginning of the whole thread - I don't think that "I'm sorry (if) I offended you" is always a non-apology. Just because someone is offended doesn't mean they're right. I learned the last one the hard way after being a victim of emotional abuse for over a year, when the other party got outraged or sad at random things to make me do whatever their wanted (and honestly, I'm not angry at them anymore - I grew to understand it was complicated and messy situation for both of us, as relationships sometimes turn out to be; the point is, it revealed a flaw in trying to atone for offending someone at all costs).