I would check what proof permission profile has been assigned to the system admin who cannot make changes in WF proof. Assuming that you are using the integrated version of WF proof, the proof permission profile can be changed in the user's settings. See screen shot below:
If the user has a 'manager' or 'supervisor' proof permission profile, they will not have admin capabilities in WF proof. You can find more information on proof permission profiles in this article on WF One here.
Hope this helps!