I don't know where to start collecting anecdotes and appeals to authority, but I shouldn't need to. See my parenthetical above--how would you go about digging through terabytes of compressed backups to find every instance of a single file and its corresponding database record so that you could delete it? It would be possible to engineer such a system, but in most cases it would be an extremely poor allocation of resources.

If you upload something to the internet and you want to be the only person who is ever able to pull it back out, you should encrypt it.