Yes, you are correct and I thought of that after I posted. But, that assumes the radiator cap which is a crude pressure control device will work the same no matter what the atmospheric pressure is.
For example a car's cooling system will run cooler with a larger radiator even though the thermostat is the same. When I installed a large transmission cooler in series with the internal to the radiator factory transmission cooler on my 95 Mark VIII, the engine ran cooler according to the in dash gauge using the same OE thermostat which is also a very crude temperature controller.