@Don: I tried a similar test using the C$ share on one of my DCs and it worked without issue, even from a non-administrator shell (my account is a member of the Domain Admins group, just as a point of information).
@Dave: When I try \\FQDN\Share from both a normal and elevated command prompt, I receive a “The network name cannot be found.” error.
Given this new information, I’m starting to believe that this isn’t a Powershell issue, but rather something else with my configuration.