That is an oversimplification. There is more defining Socialism than just healthcare. And having a solid social system in place is hardly a socialist thing.
I think their overall point is that it's possible to have sectors of the economy non-privately owned. Healthcare is a common one, but there's others - power generation, transit, education, etc.
If your definition of socialism is that absolutely all sectors of the economy are non-privately owned, then even places like Cuba don't qualify.
If your definition of capitalism is that absolutely all sectors of the economy ARE privately owned, the U.S. isn't a capitalist country.
