I actually posed this question a few months back when I realized this. Once the car is started, it can be driven without the key in proximity of the car as long as it is not shut off. So never get a false sense of security that your car cannot be driven away because the key is in your pocket and you are "just running into the dry cleaners". If you go and bring your wife the keys, it will start right up. Nothing is wrong with your car.
2011 Alpine White on Black 535i M-Sport