when the thermostat gets stuck in the open position, you won't overheat nor loose coolant. your engine will simply take more time to heat up.
when the thermostat gets stuck in the close position, your engine block will overheat and coolant will boil and evaporate. if that superhot coolant boils its way into the radiator, it might result in boiling that coolant away as well, resulting in a diminished radiator coolant level.
if boiling coolant boils into the overflow cannister, that too, shall boil away.
i think he means, some temp sending units are located in places that require moving coolant. those gauges may not correctly give an accurately high reading, if the coolant isn't circulating.
some cars are "intelligent enough", that the aircon compressor shuts down when the engine is overheating.