No, they are not, IMO, pretty well regulated - certainly not in the US, compared to, say, the EU.
The "contract" is as solid as a melting Swiss cheese, and includes the detailed fare rules for the specific fare (e.g. are changes allowed, and are they allowing a change free of charge for those requesting upgrades?) as well as the
Conditions of Carriage (in which they have gobs of gobbledygook stating why they actually don't have much responsibility for much of anything) and the various AAdvantage and upgrade use Terms and Conditions.
My view (I could always be wrong): The OP requested upgraded seats after purchasing the ticket; the OP got those seats, with no change fees, in return for proffering the needed upgrade instruments. The OP did not have the instruments, and should not have requested the upgrades if there was no intent to acquire them. The pax showed up and asked to be accommodated contrary to their request, the airline did not have seats to do so. Options: wait for seats to become available, cancel the flights or hew to their agreement, as requested with positive actions taken to request upgrades.
I am empathetic to the OP's dilemma, but not very sympathetic - as I see it, it was entirely of his own making.