Have you tried a big stick?
Seriously, you need READ and WRITE access to the central file. Even if you could turn off the visibility, people could still find it via the mapped path in the synchronization.
In short, I don't think you can.
You can control it in via your own internal policy. In other words, have a policy wereas the BIM Manager creates the local files for you - just remember to renew them to avoid stale data. I believe there is actually a tool out there that automates the creation of local files. Did a quick search, maybe this? http://do-u-revit.blogspot.com/p/revit-make-local_10.html
Here's hoping that Bluestreak brings a little better control.
