Has the water company already issued a credit? And do you have proof of the credit? If so, I would conclude that the customer has received credit and a benefit from the transaction. However, the dispute won't end there. Were there any overdraft or return item fees caused by the duplicate transaction, or interest lost (if it's an interest bearing account)? If so, those will need to be refunded to your customer.
If it is a promised credit that has not been issued by the water company then you will need to dig deeper for the investigation, and will more than likely have to issue credit - along with overdrafts, return items, and lost interest.
I reject your reality and replace it with my own.