My key assumptions are that (1) you have a functional internal network, (2) the network has at least one file server, and (3) each person who uses the QMS material has access to the network through a single-user or shared PC.
If my assumptions are correct, then the answer is to put the file copies that everyone can access in a shared folder on the server. Everyone on the network except the document control person should have read-only access to that folder, and the document control person should have full access. The network operating system takes care of permissions and other security. That way everyone can use their own computers without bothering the supervisor. It makes document control a lot easier as well, and the web page menu for the documents becomes your "master list".
If you do not have a file server, then I strongly suggest getting one - for several reasons that are oustide the scope of this area. Unitl you get one, then put the PDF files you want people to see in a separate shared folder on the supervisor's PC. The supervisor would have full access, of course, and the access for everyone else should be read-only and only over the network.
I agree with your supervisors that other people should not be able to log on to a superviror's computer and be able to do random walks through all of the business and personnel management stuff they have. In every organization I have ever worked in, snooping around a supervisor's files is something that, when you get caught, you will not get a second chance to try it.