in the system drive's root directory (i.e., click on your system icon in Finder, then click on the system hard drive and look for "backups/backupdb" in that folder).
I found the solution at this site -- nice to see I wasn't the only one with this kind of problem -- and deleted backups/backupdb. Now my install of Snow Leopard is working just fine.
So how come my system disk thought it was a Time Machine disk? Who knows... just one of those TechBlech mysteries.