Mac Pro, Mac Mini, iMac, MacBook, MacBook Pro, iPad, Displays
Finder Refuses to Delete 'Backup Items'
Status 2013-01-19: extant in OS X 10.8.2
These are not backup items; they are regular files. This is a pure Finder bug that seemingly occurs at random and is terribly frustrating and confusing.
Logging out and logging back in (or rebooting) fixes the problem.