I dont have any Tom Thumb's anywhere near me, but this definitely sounds like a major scam. It wouldnt surprise me if the card the checker used was his own personal card or someone he knows so they can reap the benefits of other people's purchases. Imagine how many people probably have no idea this is happening and this person is raking in the miles.
I would say keep the receipt and call AACS and give them the name that appears on the receipt. If it is the same as the checker, or they see that this person has unusually high activity in their AA account posting from Tom Thumb (i.e. who buys $10,000 in groceries a month?? ) then this scammer should should have their account revoked.
Thats just my opinion.

-Eli

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Washington,DC/Miami
AAdvantage Platinum