You'd need to get a PS or a Dedicated Server for that level of control. rlparker's idea is pretty sound though.
You might even consider chmoding the contents of whatever root folder your users are downloading from to read-only (0744). I'm just not sure if you can do that, because your primary user account (your staff's user account) would have to take ownership of that folder (I don't think a normal chown username:group folder would really work here) first. I can't really recommend more than that I'm afraid.
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