OK, it looks like I may have found a potential solution:
"In some cases when a file is opened from a network share that you believe is part of your Intranet zone it will open in Protected View and indicate on the trust bar that it originated from an Internet location. This could occur because of how your
proxy is setup or because you have not indicated in your Internet Options – Local intranet setting to “automatically detect intranet network.” "
I found it in a TechNet article on Protected View:
http://blogs.technet.com/b/office2010/archive/2009/08/13/protected-view-in-office-2010.aspx
I asked my users to set their intranet setting to "automatically detect intranet network"; we'll see if that does the trick.
-Kristin