Social services in the US include Social Security, Medicare and Medicaid. (Note the capital letters. Those are the names of the agencies.) And yes, they all cover citizens living in and outside the United States.

The US government makes employers (corporations) pay a large amount of money into the private health insurance system (Required by law per employee. That sounds socialized, doesn't it?). They do that to reduce the tax burden on the poor, and to maintain healthy competition in the insurance market, for better or for worse.

In my opinion, that means doctors make more money because insurance companies put the burden of paying them on big corporations that can afford to do so.

Essentially, it means the poor get healthcare, the rich pay for it, and small business owners can expense it as a reduction in tax liability.

What do you suppose you'd do if you were an employer (a corporation) with global media reach who didn't want the government to force you to pay for your workers' health care?

Well, I think you'd invest a lot into propaganda teaching people that rich corporations shouldn't pay it, the government (aka poor taxpayers) should pay for it.

And that's why so many people are under the same impression that you have (or had).