Even though the Office Clipboard can be disabled as described, it can come back again when the 'bring back the Office Clipboard' action is done unintentionally. Unless a user has read that help item highlighted by Jar, they'll probably wonder what made the unwanted Clipboard reappear.
It still seems a bit random to me, even when aware of the Office help. I think if the Clipboard is disabled for a particular document, it won't reappear. It may or may not come back for a new document though. Out of interest, play around with saved and new documents and see if you can find a more definite rule than I can

If a search is done about disabling the Office Clipboard, a number of entries come up with information on how to make the option permanent. Unfortunately, most mention a Registry edit. I expect that would do the job OK but unless you're happy about working within the Registry, it might be best not to alter anything. Since many find the Office Clipboard annoying, it's a wonder there isn't a small program somewhere that will toggle the relevant Registry entry to enable/disable it (maybe there is). Personally, I just turn it off without a second thought if it decides to pop up. I suppose there are times when it could actually be useful.
Incidentally, the Office Clipboard can be made to show by pressing 'Ctrl+C' twice rather than highlighting and copying some text twice.