If Hyatt wanted to put an end to this, it would simply provide you with the points as a customer service gesture and be done with it. You would have your AA miles "paid" by the program and the points absorbed by the program. But, it does not wish to do this and that really ends the issue unless you believe that you have a valid lawsuit in which case you will need to pursue that angle.

Whether this warrants dropping a chain is a personal decision for you. As others note, one runs out of options fairly quickly because whether or not this is a screwup, things like this will happen @ Marriott & Hilton too.