I think AA's position here is pretty simple -- OP agreed to purchase nonrefundable tickets and owed the amount agreed to. The fact that OP gave an invalid credit card number makes it harder for AA to collect, but doesn't change that agreement. Not really much different than if OP gave a store a forged $100 bill for nonreturnable products, planning to either come back and exchange it for a valid $100 if he really wants to keep them, or to just say "Sorry, here's your nonreturnable product back" instead of paying.