As I recall BMW has had a major 12V problem, especially if you take short trips, which leads to constant undercharging of the battery, and then sulfation. No radio should kill a battery after 1 minute. If the car sub systems were draining the battery so much that the small load from the radio prevented it from starting after one minute then the battery wouldn't have enough power to start the car even if you didn't use the radio.
Which is why I was stunned when I asked them to switch out batteries under warranty and they said they ran tests on the current and it was still "in spec". They literally told me if I want to play the radio I must start the engine. I didn't fight it since I had already ordered my Model S at that point. My trips weren't necessarily short either. 11 miles each way to and from work should be sufficient to charge your battery. Ironic that I'm still running into 12V battery problems with my Tesla too.