I have heard this before on old cars and newer computer controlled cars.
In olden times you manually selected the blend door with the selector that drove a cable. Same thing with the AC, Max, Vent, Bi-level, Defrost and Heat. This selector also moved the door via a cable as well, but dded switching functions to turn the compressor in the AC,Max, Bi-level and Defrost selections. Most of the cars I dealt with had a vacuum switch or other means to keep the compressor of until the engine was running. I once had a friend that couldn't start his car and we diagnosed the problem to a defective switch to turn on the clutch, it was stuck closed, so he was trying to start the car it didn't' have enough power to turn the engine and compressor over at the same time. Turned the AC to the vent or off and it started fine. We figured out the problem, but we never fixed it just had him turn it off to start the car, so he got in a habit of doing that even in other cars.
On later model cars I was always told never leave them in the AC position to turn them completely off before shutting off the ignition. I always thought this was foolish and besides I did a ton of remote start cars that you left it on to cool off the car (it's the opposite for you Yankee's). I being the person I am question everything and every time I asked someone why they thought it would mess up the AC they couldn't give me an answer. The most common response was because my _______ the auto mechanic said not to. Well I know several Master level mechanics and asked them and they said it was all a bunch of pop rocks and soda. Until I spoke with a good friend of mine that mentioned that he had been seeing problems with GM cars that the Blend door (the one for vent/floor/defrost) actuator would fail, and seemed to have them fail every few years and couldn't figure out why. After I started thinking about it I noticed on my Park Ave that I could hear the motor hunting and would notice that the wrong selection was made like I was half defrost and half vent even though I was selected to mid level. I also noticed that It would select the floor and vent even in the same position. This was after leaving it on AC and restarting the car later. I found that the gear in the actuator motor had broken (split) and replaced the actuator several years later it did it again.
Old cars no big deal, newer computer controlled cars, I think the jury is still out. My theory is that when you start your car and the system does not know the position of the doors (like after a battery change or loss of electrical power) the control module wiill find home by moving the actuators and monitoring them until it finds the correct position. Now some systems I have seen with a Pot that is attached to give feedback other systems rely only on a stepper motor to drive the door. If the controller doesn't know where it is it just steps until it reaches an endpoint and it may torque the gear and over time cause them to break (along with the normal wear and tear and just being plastic).
Anyway I have always heard this but never headed it.
Jeff