Hey, Barney. Thanks for your message.
Some "user" process is given access to the files. It isn't magically "getting" the files. Whatever it is has to connect as some "user."
Good point, one I had not considered. How can I figure out who that user is?
That's probably because you are using the unsupported NAS AFP protocol. Unless it is relatively new (or they pushed out an update), it is using an AFP hack to support Time Machine. They used a hack because Apple has never licensed AFP. Time Machine over the AFP hack has never been supported.
I don't Time-Machine to the NAS. My bad feelings about TM came from using external HDDs attached directly to the computers, and waking up to messages saying something like, 'your TM backups are unusable, and have been erased', without a by-your-leave, or any opportunity to try to fix the problem, or to try to save what was good. This didn't happen often, but it only takes once to lose many years of backup; I just don't trust TM with important things like financial docs, photographs, etc.
For 2 desktops, I TM to directly attached external drives, but am trying to use the NAS for a belt-and-suspenders second copy. I've a third copy with a cloud backup service, CrashPlan.
Only the paranoid survive
-Andy Grove, 1996
For a couple of laptops, which don't reliably always have external drives attached, I don't even try to TM.
Having said all this, I really like the concept/idea of TM. It would be a perfect solution if you could rely on it to keep on truckin'.
Stay safe.