I disagree with him, but agree with you, healthcare is not a right. As you stated, the natural rights enumerated by our constitution make no demands on others - in fact, they are the opposite - they guarantee protection from coercion by others. Anyone who believes in healthcare as an entitlement believe, effectively, that they are entitled to demand that others serve them without compensation. While there are cases where this is necessary at the federal level, healthcare is not one of them, and it's why it's not specifically mentioned in the constitution. Generally things like healthcare are better handled at the state level (and indeed, states were beginning to try before the feds stepped in). Handling these issues at a federal level enables people in the midwest to force people on the coasts to do things they'd rather not do, and vice-versa. Eventually, this leads to the kind of strife we've been seeing lately in the form of protests regarding healthcare.
Seeing how states often want to apply their rights (denying marriage equality, outlawing abortion, etc.) I don't trust them more than the Feds.
What's interesting about the current "health care reform" taking place is that there doesn't seem to be any discussion of how to actually decrease costs other than denying coverage.
There's a fundamental problem - the medical industry has made all kinds of decisions based on the assumption of high cost - doctors take on $300,000+ student debt, hospitals have built huge new facilities, and pharma has poured billions into R&D on the assumption of high cost. Rolling it back now will be difficult and will surely screw over some group of people, whether it's the elderly, doctors, nurses, hospital administrators, or hospital owners (which, due to 401(k)s, is you and me).
