I guess I'd wonder what they consider a "strong non-U.S. accent". I've had plenty of interaction with support center agents whose writing I would find impeccable, but at the same time, I could barely understand what they were saying.

I think this will be less of a problem in the future as it seems everyone (except those of us in English speaking countries) is learning English. I think the unacknowledged down-side is that we don't place nearly enough emphasis on learning other languages (in the U.S.).