I would have said so too, until I read the thread I linked. I myself had never heard "off of" until an episode of "Judge Judy" last year. se16teddy suggests that "off of" is a hypercorrection of the older word "offe", just as we sometimes hear "would of" enunciated by people who misinterpret "would've". If that is the case then what is pronounced "offa" is more correct than "off of" and equally correct to "off".
That makes me wonder whether "would've" and the colloquial "woulda" are both derived from "woulde" - but that's getting a bit off-topic.