I got this fixed by following the directions on this page:
http://www.kgarner.com/blog/archives/2008/03/31/fix-tricks-for-plugin-auto-update-on-wordpress-25/
WordPress wasn’t detecting correctly the user of the process running.
I’d like to add another $15 to the bounty on this feature’s head. I find PostgreSQL much more standards-compliant and easier to run than MySQL anyway.