Understood.  However in this case I needed an external config file as it contains metadata about a fileset that comes from somewhere else.

In any event I solved the problem.  And this is a rather obscure glitch for those of us out there that have to use package deployment.
My UNC was in the form of \\servername\SubfolderA\SubfolderB\SubfolderC\myconfigfile.dtsconfig.
I actually had full access rights to SubfolderC and the package itself had a vb task that reads up the contents of the actual config file as proof of my access, HOWEVER, it turns out I wasn't given rights to list folder contents of "SubfolderB".  SSIS must be doing some sort of reading up of the folder hierarchy when setting the config.  When it gets to SubfolderB it can't see what''s in it and then chokes.  Once the network folks gave me these rights, it ran just fine.
Another quirky SSIS bug...