The whole plan was for the single-payer, two-tiered system. It’s all run by the government, but there are the “preferred” providers for the nomenklatura, and then third-world class care for the peons.
It usually works out pretty much that way in the nationalized medical care systems. In Canada, though, I've heard of even political bigwigs there coming into the US for care they thought was better than their socialized system could provide them.