Update:
Still having the same problems. I have given the user Read/Write access to the entire C: drive after running FileMon and finding that MapPoint appears to access the C: drive alot. Also, I have searched the registry for any key which mentions MapPoint or PushPin and given the user full control to them. I still cannot get MapPoint to open the PushPin Add-on when logged in as the user.

Does anyone have any ideas? We cannot give the user admin rights on her PC, it is against company security policy.