We've had a request to grant limited (Read, File Scan) rights to
a folder on the network. However, there are concerns that files
that are viewed in the folder could be saved into another location.

I'm inclined to think there's not too much that can be done about
this--if they can view it, they can save a copy of it. . . .

But--in case I'm missing some option, here--I'm wondering if
there's a way to do this.