Whether you win or lose a chargeback has no connection to whether an error occurred. Visa/Mastercard establishes liability between the merchant and the bank. Reg E establishes liability between the customer and the bank. All of the information Western Union supplied in this chargeback could have been compromised through a data breach at a merchant your customer shopped at, through a phishing email your customer fell for, or through a hack of the customer's personal computer.
If the charge was initiated from a geographic location other than where your customer resides, that is evidence that they did not authorize the transaction. I don't see that you have enough evidence to deny the claim. Your option for recover is to explore the prearbitration process with your card processor. If your customer can provide an updated dispute letter noting that they examined the merchant's compelling evidence and that the IP address from where the charge originated is not their computer and that they still dispute the charge as fraudulent, you may have recovery options from the merchant.