In the Backup process there is a screen that asks the Teacher what they want to back up, and gives a choice as to the course, sections of the course, Users, User Data, User Gradebook and so on. Checkboxes are provided to select or deselect for inclusion or not. If that screen is not appearing then the Admin can go into the Permissions table via the Site Administration menu and reset the required User permissions (try Users > Permissions > Define Roles - and be careful you are not on the Front Page Permissions).