Hmm. That's the meaning I usually hear it used for. What other meaning are you talking about?

The other meaning is referring to something that is racist/sexist/etc. I suppose technically that's still "inducing disgust" but it's different enough to be considered a separate definition. For instance, I'm offended by the state of some of the code at work, but I'm not filing an HR complaint about it :)

I always took that usage to come from the idea of offending one's sensibilities.

That's also how I took the author's use of offensive i.e. it offended his sensibility that mid-Atlantic has two meanings (or whatever it was that he was offended by).

I read it as he doesn't like the accent, and doesn't like that it's associated with him. It's a joke, a pun on the two meanings of "mid-Atlantic"