It's funny, because I almost always use UNC paths. For some reason years ago when we bought this program (a canned Payroll/HR package), the vendor set everything up with mapped drives and we stayed with it ("if it aint broke, don't fix it" type thinking).
I link to their data all the time, but when this problem cropped up, I couldn't figure out why it would work one way and not the other. Your explanation in post 10 was pure gold, and I understand now. It's nice to know the "why" in addition to the "what".
Big thanks to you and rdjabarov for digging me out of the hole!