Had a customer purchase a large/oversized item with 2nd day delivery. Cost was around $100 in shipping and I put signature on the package due to value and not using Buy Shipping as I got a cheaper rate. Customer emails me on delivery day stating that the package was damaged and carrier would not let him inspect it without a signature so he refused the shipment.

Package comes back to me (with an unknown amount charged for return shipping). Shipping box is not damaged, just normal wear from traveling across the country in an airplane both ways. I open it up and nothing is damaged as I bubble wrapped and padded it well enough. Customer has already filed an A-Z claim at this point stating they have not been refunded and the claim is for "package didn't arrive" with the notes in the claim "It seems that the customer mistakenly filed a claim for an issue with a not received item, but the actual issue is return-related. While we acknowledge that the customer hasn't submitted a return request, you must provide a return address so that the item can be sent back."

What would you do in this case to reduce the chances of a full refund from A-Z and a metrics hit?