The link is dead, but I did my own research to find that legally you are right, but the government still works in a capitalist system. If they did get rid of some of the government controlled areas, they would do better, however even if China nationalized health care, I doubt it would make a monumental difference.
Plus, this comes down to lives. Everyone should get care, if life saving or an Advil for a headache. For me that is the most importent, and we learn how to fix the rest.