I guarantee you will run into a stone faced person
when you try to check in at AA if you don't have that passport in hand ready to go. Full stop! No exceptions and no 'flat tire' rule. What they do with you after that and what they charge you to go on another flight is up to the manager at the moment. I've had colleagues whose papers were not in order and they were not allowed to book another flight until they had their papers in hand for inspection.