Rights are defined as part of the social contract we create in living close proximity to each other. If the collective people define what their rights are through democratic representation, then it's up to those who have the monopoly on violence to enforce it.
The "Stand in the school house door" is one historical example of this in play: https://en.wikipedia.org/wiki/Stand_in_the_Schoolhouse_Door
It's obvious why people are in favor of them of course, but we have to be honest about what it is we're asking for and why instead so we can make a rational analysis of it, instead of torturing the intellectual and moral foundations of our culture to make something outside of it fit. And it's foolish not to be suspicious that politicians' incentives have basically everything to do with making promises that get votes, and basically nothing to do with actually making the system work long-term.
Whether or not healthcare is a right is a lot less important than whether or not it is affordable.
Via its taxpayers of course.