How do I bypass the user permissions error when accessing maps that have been created by other users?

NTM maps credentials are saved PER user thus other users has no rights to read the map. All credentials are stored in per Windows user credential Vault, you can view it from Control Panel\All Control Panel Items\Credential Manager.

To let other users view the map, you may try logging in using your windows account that can open the map and simply click "File -> Export -> Map" and give the map file a new password. This map can now be open by other users using the specified password.

Hope it helps.