If the delay is AA's fault (such as a mechanical delay) AA will pay for hotel and give you food vouchers (which normally cover about half the cost of reasonable meals). If the delay is not AA's fault (such as weather or ATC delays), AA will not pay for hotel, but at many locations AA will give you a piece of paper entitling you to a "distressed passenger" rate at an airport hotel. If that hotel has rooms free, this rate will be )in my experience) about half of what you could book for on your own. AA will arrange onward flight to your destination, but will not necessarily put you on another carrier. My experience with your second scenario (another airline is late, so you miss your connection with AA) has been similar to pure AA situations for flights, but the hotel/food part is dictated by the policies of the other airline.

I agree with emma dog's appraisal of Chris Elliott. One obvious question that Chris didn't ask was about the English skills of the passenger he was reporting on, who was visiting from Japan. If this passenger had difficulty with spoken/heard English, it is possible that they were misunderstood. We have all experienced the situation (many times) where someone is getting close to departure and is moved to the front of the line for check-in or TSA screening. When I see this, it is not because the lines are incredibly long, it is because the passenger did not allow enough time at the airport, so their failure to plan properly becomes a reason to inconvenience other passengers.