BrianC is the Reg E expert, so maybe he will weigh in. But here is my opinion of the matter.
4 questions:
1) Was this card was ever reported as lost/stolen?
2) Are these card present transactions?
3) Do the disputed transactions and the number of monthly charges appear similar to the established pattern of charges to this merchant?
4) Does this customer have a history of frequent disputes? Not that this can necessarily be used as a denial reason, customers who frequently dispute have generally figured out "the system, so this can become an indicator.
While a counterfeit card isn't completely out of the question, those transactions generally occur somewhere far from your customer.
In your review of statements, and by his admission, this is a gas station he visits often. You have an established pattern of usage, a customer that admits to frequently visiting the merchant, transactions that don't appear out of the ordinary, and are more or less the same as transactions spanning back to 2015. So you have 2 options:
1) If you aren't confident that the number of transactions per month and the amount of the disputed transactions do not match the history, your safest course is to cancel the card, refund the amounts, and refund any fees which may have occurred. Remember you also have the option of not issuing a new card.
2) If these match with transaction history, you might try to get some signed receipts of the non-disputed transactions and compare those signatures against the signatures of the disputed transactions. Failing that, if you're confident the transactions remain true to the established pattern, you may have enough reason to deny the claim. Be sure to document, document, document, and document some more.
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I reject your reality and replace it with my own.