Rule 1 - The customer is always right.
Rule 2 - If in doubt see rule one.
Sorry, I have to side witht he customer on this one, even if the complaint may chafe a little. The guy did pay like clockwork on Paypal, so it seems that a little of the same level of urgency is not our of the question once someone has their money. He has a legitimate beef.
The best advice I can offer is that a complaint like this is a favor extended and a window of opportunity on how to perform better order fulfillment and customer service.
Remember, I did agree that it might chafe a bit, but that is probably because the arrow found its mark a little bit.