Nationalization = government ownership. Regulations + purchase mandate ≠ government ownership. There's one more step but I think you can figure it out on your own. Examples of nationalization in modern times: You could say AIG was "in essence" nationalized. You could say GM was partially "nationalized" (Dept. of the Treasury has a 61% stake).
Nationalization is EFFECTIVELY so when the govt. has all the rights of ownership, even if it owns 0% of whatever it is.
The government has no more rights of ownership in health care than in any other industry they regulate. Mandating you buy something by way of a tax has nothing to do with ownership rights. The government regulates almost everything that exists. All car companies must comply with a ton of regulations. Does that mean the entire auto industry is effectively nationalized? Even Toyota has been effectively nationalized by the US government? The administrators of health care and insurance companies are all still private and get to make the lion's share of the decisions. Just because they are regulated doesn't mean they are effectively nationalized.
What's the difference if the govt. or "private" company makes decisions, if those decisions are mandated and overseen by a govt. board? None. The automobile industry is not effectively nationalized at this point (GM is), since there's no law requiring you to buy a car. The automobile industry WAS effectively nationalized during WW II when the vast majority of the auto plants' output was planes, tanks, jeeps, and those sorts of things.
