UPDATE:
In the end, if you can't trust the users of your system, they will find a way to thwart whatever security mechanism you put in place. It's just that simple.
As the saying goes, loose lips sink ships.
On that note, you can make it harder for them to do so. Based on what you have described the only thing I can think of at the moment that would be feasible for you is some kind of one-time authentication system or maybe even smart card authentication. However, even these solutions are probably overkill for protecting a "NAS". That and the chances of the NAS software/firmware supporting these features is unlikely.
ORIGINAL ANSWER:
If the device supports it you could setup an IP address whitelist, though this isn't completely full proof. It would still allow anyone behind a given address access to your server. It does prevent everyone else though.