Therin lies the difference between 'human rights' ad I guess what would be better termed as 'guaranteed services'
The rights outlined in the Bill Of Rights, for example, are of the nature of simply saying "this is something that people should be allowed to do, and therefore we, the government, will not attempt to stop you from doing it", Speech, Exercise of Religion, Assembly, etc...
None of them really obligate anyone to actively do anything, just stay out of the way and let people get on with it.
In a very real sense, as a human rights issue, we already have universal health care as a right in the sense that everyone *may* get health care and the government does not actively attempt to interfere with people accessing it.
However, if you are now talking about guaranteeing health care services to be actually provided to everyone, that's quite a bit different. It goes from "we're not going to stop you from exercising your right" to "we have to do something to ensure your right". While you can say that some rights must be enforced, so to speak, it's easy to see that they are not the same.
Free Speech is easy; and the less government involvement you have, the easier it is to do. And if the government is involved only to the point of keeping others from infringing on that right, that's the best you can hope for. Free Medicine is different. It's not something that the state just 'let people do' but it has to be something the state goes out and does.
Which is where the comparison breaks down; which is why you can say "the more free speech, the more powerful that freedom is" and maybe not say "the more free medicine, the better quality that medicine will be"