Actually BAP is a very poorly written RENTAL agreement for the HV battery. And per your comment, it does not cover the 1yr/10k service (or subsequent milestones) as that is an out of pocket cost item to the lessee . . .. . . it's a lease agreement.
The 10k mile service has nothing to do with the drive battery. The 10k service is literally checking to make sure your lights work, topping off fluids, changing the cabin air filter, and of course the most rediculous of all... Changing the key fob batteries.
Listed below is from a Daimler/M-B/smartUSA BAP publication dated 4/13.
battery assurance plussm?
battery assurance plussm creates a truly relaxed electric drive experience. instead of a conventional lease, finance or purchase of your entire smart electric drive vehicle, including the battery, battery assurance plus allows you the option to lease, finance or purchase your smart electric drive and rent the battery separately.
besides peace of mind knowing you’re doing your part to care for mother earth, battery assurance plus includes:
>> lower cost of owning or leasing the electric drive vehicle
>> guaranteed battery capacity of 41.6 Ah, up to 10 years
>> annual maintenance of the high-voltage battery, up to 10 years
>> battery repair or battery replacement, if defective, at no cost (should it ever be necessary), up to 10 years