Now that you are on Mountain Lion, you can boot to recovery mode and re-erase the entire Macintosh HD (or whatever name the OS volume has). Perhaps your definition of clean install didn't actually clean the offending apps or you are connecting another hard drives with apps purchases from the previous owner's account. (The app store will offer to update any apps it sees, not just the ones in /Applications)
Here is a long article on recovery, but details at the bottom show explicit steps you would take to prepare an external drive to install Mountain Lion. You will want to perform those steps from Disk Utility when booted in recovery mode.
Note, that if the previous owner had "redeemed" the iLife apps (as described in the article above), those will remain tied to their account so for you to install them, you will need to purchase iPhoto, iMovie and GarageBand since they are not part of the Mountain Lion software upgrade you purchased, but after a clean wipe, you won't have those applications and could only see them if you had a copy somewhere other than the wiped drive or signed in to see past purchases for that previous account.