Technically AA was correct (the pax did not have valid travel documents) even if it was for the wrong reason as most would assume (I really doubt AA enforces US exit rules, as they have no risk in such).

I would beg for mercy, mention the AA misinformation, and hope for the best.If the OP wants to play hardball, the only issue I could see would be camera/video/phone incedent.

I would also .....slap the cousin for not immediately getting a valid passport, at whatever cost (though I guess the OP might need to play nice with the wife).