Thanks for the replies. I ended up doing something like what was described in
's post because I ended up looking at the printed owner's manual (how quaint!) and saw something similar. I didn't have it in front of me but I remembered to put the car into reverse. I think one also had to hit the "M" button on the door, then the side view mirror button, then put the car in reverse and do the adjustment. Anyway, whatever I actually did it worked.
BTW the Automatic mirror folding (which I have ON because it's a handy way of figuring out whether you've locked your car, at a glance) is just for when you lock your car. It doesn't have an effect on the "tilt down while reversing" thing.