Repeat after me, from the first chapter of "THE MAN BOOK," ....
"Yes, dear, I was wrong, dear, you're right, dear."
Seriously, I would say it's fine to apologize for wording it in a way that caused her to misinterpret it ... that way, you're saying it's you're fault that she can't understand you. She may like that, as it fills her need to be right.
However, in the long run - and I don't know how serious the issue was that she misunderstood - but, in the long run, if she's that touchy, and that insistent upon you saying you are wrong and apologizing, she may be a disaster waiting to happen.
... for you ladies out there who may think I'm dissing the female gender, please read further ...
... I honestly think women are the crowning creation or the greatest result of evolution or whatever .... but, I'd say the same thing if a woman wrote that her BF was doing a powertrip and insisting that she apologize for something he misunderstood.
When either party of a relationship can't just say, 'ok, I misunderstood, but I'd be really PO'd if you had meant what I thought,' then I think that person has some issues that make a meaninful relationship difficult to imagine.
No one is a mind-reader ... and if he / she cannot accept that the other did not intend the comment as they interpreted, then I think that's a red flag. Maybe not a deal-breaker, but a warning flag. And too many warning flags mean a hurricane is on the horizon.