Will the computer on a Tesla allow the batteries to be deep discharged to the point of doing damage?
I doubt it. Mostly the concern is, keeping drivers from running the batteries down too low to reach any place where the car can reasonably be recharged. That's just smart marketing. But the charging will slow down if the batteries get to some specific temperature, but also to protect the charger itself. As the root article for the topic notes, these new model Superchargers have a cooling system for the cables.