It sounds like you have evidence that your customer did not receive benefit from this transaction. The address mismatch would seem to indicate that your customer also did not authorize the transaction so you have enough information to conclude that an error occured and you owe the customer the money.
The address and IP mismatches givve you the ability to file pre-arbitration to recover the funds for the bank if your customer is kind enough to write an updated letter that refutes the merchant's compelling evidence.
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