The fix posted by dd@sucuri in this thread seems to have worked like a charm for my affected site (I'll link to the page with the fix here in case impatient people are skipping to the end of this thread).
For the record, all of my wordpress sites have been running 2.9.2 since its release, and only one site was affected by this latest b.s.: the one hosted on a shared linux server at GoDaddy. My friend's BlueHost sites were fine and all the sites on my own server were fine. So GoDaddy's statement that this was a problem affecting only people running outdated versions of WP is just ridiculous.