Regardless of how the unauthorized transaction occurred, it's your customer and you are responsible for investigating under Reg E to determine if an error occurred.
V/MC have chargeback rights for filing chargebacks when a merchant processes a card multiple times without authorization which you can use to recover the funds for the bank.
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Sola Gratia, Sola Fides, Sola Scriptura, Solus Christus, Soli Deo Gloria!
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