"This is proven daily in the influx of people from nations with socialized health care coming to the US to receive health care that are unavailable in their own countries."

I would have thought that this would occur because the US is such a large wealthy country, with huge resources, finances and access to advanced technology, and an abundance of medical professionals.  The fact that some medical procedures are not available in some other countries would have more to do with the lack of those very things I just mentioned, and not the health care system.