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Finder Refuses to Delete 'Backup Items'
Related: Apple, Apple Core Rot, backup, how-to, macOS, macOS Finder
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.