Further, A "no refunds" policy is for buyer's remorse or "as-is" sales. Since the card was used without authorization, the OP is not the buyer.
This is similar to someone using a stolen card to book a no-refund airbnb. In no way would we expect the card holder to "pay for their mistake" of losing the card. The host refunds the money, or airbnb refunds the money, and the card holder is made whole.
I actually disagree with you here.
The criminal and/or insurance should make the cardholder whole, not the other party in the transaction. The cardholder should notify their card company of the fraudulent charge and let them investigate.
I always get asked "Have you contacted the seller yet?" when I dispute a charge.
Since we're making up new scenarios here, I'll use one that might make it clearer why I disagree with your AirBnB one. If the teenager who made the unauthorized purchase had instead ordered 60 pizzas for a pool party and those pizzas were in fact delivered, would you expect the pizzeria to give a refund to the card holder?
No, the pizzeria did their part of the transaction and had no reason to suspect that the charge was unauthorized. Otherwise, the loss shifts from the cardholder to the pizzeria who spend resources to make those 60 pizzas and they don't get that money back, whether or not the pizzas were eaten.
Fair enough. We know the pizzeria doesn't eat (har!) the cost but we also know that the card holder doesn't either. Most likely, in the end, the bank does.
However, in the OP's situation, the item still exists. The seller has it. Nothing was lost except some time mailing out the package.
Let's go over the "correct" thing to do here. Is this it?
1) OP disputes the charge.
2) OP gets the kid arrested.
3) OP follows the "no return" policy and keeps the item.
Result:
1) OP doesn't pay out because OP didn't order the item in the first place. Yay!
2) Kid learns a lesson. Yay!
3) Seller...learns a lesson (confirm with the buyer first)? Yay?