Weird turn of events on this. My indie says they charged the battery and it holds a charge no problem. He says there's nothing wrong with it and that I must have left something on to drain it over night. I'm fairly certain I left nothing on, although as I said, the alarm did go off for no apparent reason.
Should I get a second opinion on the battery? These guys are pretty good and know BMWs, but I'm still at a loss to explain the dead battery.