Almost sounds like one of your cooler lines blew. Did the shop tear the tranny down? If not I don't know how they could diagnose internal damage...at a minimum they need to drop the pan.
The rubber hoses that connect the hard lines to the radiator are notorious for becoming brittle with age and breaking/leaking. I would check the lines, replace if needed, fill her with fluid and see if that does the trick. Way cheapee than their "options". Good luck.