I think you are right. I'll suggest that they replace it since I doubt there is anyway they can diagnose the problem. The SIB for the Excessive battery drain takes 6 hours so they'll have the time.

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2012 F10 550xi Carbon black/oyster
2011 E92 M3 SSII/black
2012 W166 ML63 Steel grey/porcelain
2007 E93 monaco blue/beige (retired)
2010 E70 35d Space grey/saddle brown (retired)