OK, so they are charging $600 for enabling the Supercharger software to give you access to the Supercharger network. (The hardware is the same between both and you get CHAdeMO charging included when enabling Supercharging.)
I wouldn't be surprised if the Tesla CHAdeMO adapter converted the CHAdeMO protocol into the Supercharger protocol to make it easier for Tesla in only supporting one DC fast charging protocol in the car.
BTW: I never said that they guaranteed access with no restrictions, but the pages does just say "When Supercharging is enabled, Model S drivers can charge for no additional cost at any of Tesla’s expanding network of 120 kW Superchargers." and that doesn't hint at
any restrictions. And the pages that it links to has a
FAQ: "Q:
How much does it cost to use the Superchargers? A:
Supercharging is free for the life of Model S, once the Supercharger option is enabled." Again, they say "free for the life of Model S", no restrictions mentioned. Seems pretty clear to me.