I'm still having a problem with this. At sea level the air pressure is 14.7 psi on a diaphram which is opposed by a spring in the regulator to produce 11" WC. As you increase elevation say to 6,000 MSL the air pressure drops to 11.8 psi, but the spring is still exerting the same pressure.
This tell me that the output pressure would have to increase. It would be the same as increasing the spring pressure at sea level while maintaining the same atmospheric pressure which increases the output pressure.
I know that my appliances still work at high altitude, but that is not the question.