I think you misunderstand. The supercharging session is handled through the cable obviously. The latency/reliability of 3G/4G is not enough to do that practically.
However, the VIN information is not used by the superchargers even though it is transferred. All the access control appears to be done on the car side, at least from what wk057 found back a while.
So the permission for free supercharging and also billing for supercharging appears to be handled on car side (no different than activation of other features like autopilot). Of course they can change this to have some sort of processing on the supercharger side.