Indeed Healthcare is no more a right than Liberty or the sanctity of owning property which become rights when men (sorry girls, but it was men) declared it thus. I would argue that hierarchical domination is the natural order within human and similar branches of the animal kingdom, and that individual "rights" ascended only through the organization of society and the extension of laws to guarantee present cornerstones such as freedom and property rights. Healthcare follows in this vein of argument. Liberty, (and in other nations) universal health insurance covereage and public finance of basic insurance for those unable to pony-up, are not naturally-conferred, but societal constructs not as a result of their ordination by a deity-of-choice, but because they yield meaningfully large positive externalities far in excess of their costs.
I genuinely like the reasoning here. One cannot deny the historical succession of certain rights: personal liberty --> property rights. I also agree with the author that they are not 'insert-deity-here'-given, but established by man. The French Revolution, ratification of the Constitution of the United States - all fundamental milestones in the development of our society. Based on this, it is reasonable a suggestion to make, that maybe it is time to take the next step: property rights --> healthcare.
But... Yes, there always is a 'but'.
Liberty and the right to property are non-intrusive. They merely define our personal space and the set of actions we are permitted to pursue. A good rule of thumb here is that we are free to do whatever we want as long as it is not in conflict with the freedom of others. The 'right to healthcare', on the other hand, legalizes a wealth transfer between the ones who require healthcare and the ones who are forced to pay for it. It infringes on personal liberty and right to property of the reluctant sponsors. Therefore it is not a logical next step, increasing the degree of our freedom - in fact, it is partially dismantling it. Or at least transferring it.
And one last thing - I could just as easily state that 'the negative externalities of limiting or transferring freedom are far in excess of any of the benefits of universal healthcare coverage'. Simply stating something is true does not make it so and is... how do I put it... childish?
In conclusion - a noble attempt, but I remain skeptical.