That was originally true. Although the car passed the VIN to the supercharger as part of the conversation, however it appears the supercharger didn't so anything with that info. The VIN passing appears to be there for future authorization/accounting usage.
So the sole factor in determining if the car could supercharge was based on the configuration of the car itself, which someone with root access could toggle. As far as I know that global toggle within the car still exists, and may still be how Tesla disables supercharging for salvaged cars.
Since that time, however, Tesla has moved to a pay-per-usage plan. That plan also grandfathers in "free for life" folks, as well as allows for some initial free credit each year. As this would have to be tracked per-car, I believe it's now done via that authorization with the supercharger. I've not seen the decodes since that was implemented, thus it's plausible the car itself talks back to HQ instead, but I doubt it.