You might as well be running Windoze.
I'm running a Novell shop out here. I can restrict access to any directory or file I choose based on group memberships, physical location on the network, IP address, MAC address and right down to the user him or herself.
If you don't already know how to do this, then you shouldn't be a network administrator. It can be accomplished with WindowsNT, UNIX, Linux, BSD and my baby Netware.
Without having any clear indication of what NOS you're running,I can't even begin to tell you how I'd solve your problem in your particular situation.
Now, about you not having access? That's actually doable. Just create a location on the server with granular permissions that allow someone, other than yourself, to gain access. Again, if you can't figure this out, or even know how to do it in theory, then you need to be in another line or work.
However, if you run a tape backup like ArcServe, you will need at leat one ID on the network that can access all files in order to back them up. Other than desiring some sort of disaster recovery plan (backing them up) there's really no other reason to place sensitive materials on the network.
As far as backing them up, just buy your boss a CD burner, JAZ drive, Ditto drive any kind of external media drive and teach him how to use it to back up those sensitive files. Lock them in a fireproof safe and your job is done.
Oh, and you need to establish, and do so immediately, that IT policy isNOT dictated by management. They can pay the bills and refuse to pay the bills, but as far as HOW a network is run...that's your job, pal. If you can't get that authority for what you're surely going to be held responsible, then you need to leave and work somewhere else.
-Jake