Have you experienced this personally, or do you have this on first-hand account, or are you repeating the common wisdom?
Because like I said, Lynx had a way of doing this circa 1999. It mostly ignored tables except a few that met some criteria for likely semantics. So you generally got a cell-ordered page, which worked surprisingly well for most sites. Heck, if you've got a copy of Lynx at hand, fire it up right now and browse HN (which is layed out via table, ridiculous though it is for a site with such a simple layout).
If Lynx can do it, I have trouble believing that deliberately assistive software wouldn't be able to. This matches most of the (admittedly limited) discussion I've had with people who use/write it (an aside: I've also heard that, believe it or not frames were sometimes a big boost to assisted usability).
If you've got personal experience or first-hand accounts, though, I'm interested to hear it.