It's normal to see surface rust on the rotors after washing, however, I have never heard of the rust causes the wheels to lock up

The solution of drying the brake to prevent lock-up by driving around the block is laughable

You have an AMG for crying out loud and you have to dry your brakes like that to prevent wheels locking up after a car wash? The service manager suggested that should go back to school for basics.
You definitely have a problem and the situation is NOT normal. No surface rust beween the rotor and the pads can make you wheels drag three feet before breaking free. See another dealer for solution