My friend's American made car had the same extact problem. The battery was fine and the altenator charged up perfectly when tested. The problem was with the diode in the altenator. It drained the battery after couple of days of inactivity. When they first tested the alternator they only checked if it charges. AutoZone can check if the diode is faulty as long the altenator is still hooked to the car. He changed the whole altenator and the car runs fine now.

They might already checked for that considering you took it to MB dealer but I thought it never hurt to mention it.