I flew ATA only once - LAX-MDW.. and even thought it wasn't the airline's fault, there was a criminal on board the aircraft. Some guy stole one of the FA's purse (she accidentally left it on a seat).. they knew exactly who it was and all she wanted was her checkbook and credit cards .. he could keep the cash and they would keep quiet.. but he chose the hard route. The cops were waiting for him at the gate.

The moral of this story? ATA can be really cheap.. but keep in mind that petty criminals are probably cheap too.