Usually? Which ATs are you describing? We care about this sort of thing and weren't aware of that constraint - a quick Google doesn't highlight any obvious issues with Jaws or NVDA, except for this [1] in 2003. But since then there have been huge changes in assistive tech - pretty sure the whole ARIA thing didn't exist back then, and there's probably more choice in ATs now than ever before.

1. http://www.velocityreviews.com/forums/t155840-nesting-inside...