Really? Who's supporting single-payer healthcare again? What is that, if not the nationalization of the health care industry?
The nationalization of health insurance, actually, not the health-care industry.
Everyone except anarchists supports socialism in some parts of the economy. If nothing else, everyone supports a socialized military and law enforcement. A genuine socialist supports all or most of the means of production being publicly owned. Those who don't, aren't socialists.
Pretending those links don't prove you wrong does not make it so.
I'm not pretending anything. They don't. They don't prove anything. And you claiming a blatant falsehood does not turn it into a truth.