Well, since no one else has any ideas...
I finally found the answer to this problem on tech-forums.net. Here's the URL:
http://www.tech-forums.net/computer/topic/3435.html
It references a Microsoft KB article 304624:
http://support.microsoft.com/default.aspx?scid=kb;en-us;304624
The problem is that Windows XP automatically caches redirected folders. So if your DC has ever redirected your "My Documents" folder (or Application Data or Desktop or Start Menu), you may see this effect. In order to undo this behavior, you have to disable a local policy on your XP machine using MMC. Here's the cookbook outline:
Click Start > Run
Enter "mmc"
Click OK (a blank MMC console starts, probably named Console1)
Click File > Add/Remove snap-in...
Click Add (Add Standalone Snap-in appears)
Select Group Policy from the list
Click Add (Select Group Policy appears)
Click Finish (take the defaults)
Click Close
Click OK
Expand Local Computer Policy > User Configuration > Administrative Templates > Network > Offline Files
Double-click "Do not automatically make redirected folders available offline"
Select Enabled
Click OK
Click File > Exit (you don't have to save the console, if it asks)
Reboot
You should now be able to pin and unpin files/folders at will.
Hope this helps,
TomC