Once one grants that healthcare is a right (presumably meaning  universal health care), then effectively one accepts that a very particular type of health "insurance" (single payer) is a right, or the next best thing to a right. Since the proven least expensive way to provide universal health care, is some sort of single payer system eliminating profit and the enormous cost of claims administration.

Even if the single payer is the government, and even if no invoices are issued to patients, and even if there are no premiums to cover costs (as when costs are paid out of general revenues) we still have effectively an insurance scheme...a very large number of people pay into a pot out of which claims are paid. 

In a capitalist society with an instinctive desire to keep costs down, the moment a polity embraces the concept of "universal coverage," the notion of single payer follow as virtually self evident. The only exception is "additional" insurance for extended coverage.