"Human rights" are poorly defined, but I guess the closer we have to a formal definition of them is Universal Declaration of Human Rights which does include health care and right to education at the same level than free speech or fair trial.

But I agree it's a very poor defense of universal healthcare, the UDHR is a political document that can carry weight of authority, but it doesn't make something ethical or unethical by itself. The only way I use the UDHR in a political discussion is with a reasoning like « UDHR includes right to healthcare, and UDHR was accepted by most countries of the planet, so it's not a completely lunatic position. Now, please stop your authority arguments like "the only natural rights are freedom and ownership" and listen to my actual arguments for universal healthcare, and I'll listen to your real ones against it », which doesn't in itself justify healthcare, but can help giving me at least a chance to expose my arguments.