Hi,
Create another user account with the exact same user groups and you should see the same thing as him.
Note that if he is in several user groups he will have access to all the shipping methods of all the user groups.
So if he was in the "registered" user group, and you added a new user group to his account, and you configured the UPS shipping methods to be available to all the user groups except that new user group, then it's normal he still sees it as he is in the registered user group which has access to that shipping method. You would have to remove him from the "registered" user group and make sure that this new user group has the same joomla ACLs as the "registered" user group so that he can still login on the frontend like other users.