I had one boss who decided that we needed redundant systems and bought in a new server infrastructure with mirrored servers in two separate server rooms, separated by a physical firewall (a wall to stop real fires from burning down both server rooms).
So far, so good.
However, he was of the opinion that, as we now had mirrored servers, we could do away with the tape backups. The whole IT department said no, this wasn't sensible. But the boss said that it was no longer needed, as we had a hot backup.
No amount of trying to inform him that a hot-standby redundant system is not a backup could get him to change his mind...
Until one day he made some changes to the main database and corrupted it in a catastrophic way. He said, no problem, pull it back from the redundant machine... At which point he learnt the hard way that redundant means that everything that happens on the primary machine also happens on the secondary machine "at the same time", which meant that there was no "backup" of the database, just an equally corrupted database on the secondary server!
Lesson learned, he agreed that making backups was a good idea.