Sounds plausible, it's true that the car would be in ready mode with the keys are near by. The questions is, what is the distance? Are your keys left near the car at home or work.
I used work in the mobile phone industry and I had a guy once have a bluetooth car kit fitted by a 3rd party who just connected it straight to the battery so it would remain on constantly. His bedroom was right beside the garage where he parked the car. So the phone would stay connected to the car kit all the time and it flattened his battery in the car real quick. He only realised one day when he went to answer his phone and it went through to the car kit. He said the next day his battery was dead.
So I guess it could happen, the only option I can think of is put your keys away from your car.
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Ford Mondeo Zetec Hatch in Blue Ambition
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