If the the flight went mechnical and it forced an overnight AA must provide lodging. I'm having a hard time believing that there were no more hotel rooms or AA would not pay a certain rate (AA gets corporate rates at the chains anyway.)
Moreover, this is the reality of airline travel. Overcrowded flights, no overabundance of spare a/c, inadequate staff at the airport to handle problems, etc. One, never check bags. Two, become an elite, preferrably at least mid level, so you have a least someone in CS to assist you if you are going to fly regularly.