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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.

Finder bug requiring reboot or logout: cannot delete backup items
(“The operation can’t be completed because backup items can’t be modified”)
(“The operation can’t be completed because backup items can’t be modified”)