I think the answer of you guys was not totally correct. Most modern cars have an automatic AC control, which basically (depending on the way how it is programmed) will either allow only a maximum airflow in the car (so that a certain airflow is not exceeded to discomfort the driver) or to ensure to reach the cabin temperature of choice in a certain amount of time. However, when the A/C is set to run in this automatic mode it can make a difference since the computer is adjusting the airflow and the A/C compressor output power depending on the output temperature of the A/C).
Most of those A/C can also be put into a manual mode where you can adjust the air flow manually. In this mode I agree with you guys (but only if it set to maximum). Then it shouldn’t really matter if you set it to 60 or 70deg b/c the compressor will run full blast from the beginning. However this might not be true if you don’t set it to full blast.
So IMHO, depending on which ‘mode’ the A/C is set, and to what the air flow is set (if in manual mode) it makes a difference.
Not sure if that helps Peter, since depending on what mode the car is set to, when they choose the temperature, it could be that Peter or his wife is right/wrong.