Richard - Your scenario shows why 2 backup copies are not enough.
          It's just too easy for bad copies of a file to overrun
a small backup retention quantity before someone notices the data
bad and seeks restoral of the most recent good copy.
    I'd recommend not bothering with permissions change machinations
in that other factors can also cause additional backups that are
unwanted (small change in file name, for example).
       Richard Sims, BU