This was likely an honest misunderstanding between the salesman and your parents. In order for the work order paperwork to be created at the tire center service desk, an active Sam's Club membership card has to be scanned to access the menu screen. If your parents had accompanied you to the service desk, they would have performed the balance/rotations for free per the warranty. I have purchased tires at Sam's Club for my (non-member) parents for nearly 20 years and they have always performed rotations, re-balances, and flat repairs for free on my parents' vehicles when I accompany them and present my membership card.
Nowadays, you are not even allowed to enter a Sam's Club or Costco store without showing/scanning your active membership card, much less access the tire center service desk.