Agreed. P0125 is low coolant temp indication which leads one to believe that the thermostat was stuck open.
The bill said P0124, but given your observation, it was probably a typo.
She also said they told her it cost $167 to read the code and reset the light.
I still think $344 is pretty steep for replacing a thermostat and coolant. My guy (ASE certified, full service shop) said he'd have done the work for about $120, Motorcraft thermostat & gasket included, including testing the cooling system for leaks. His oil/filter change would have been $22. -- Buckle Up. It makes it harder for the aliens to suck you out of your car.