Yes, healthcare is a human right. It is important that, as medical advancements are made, they are made available to the general public. This includes cost as well; with a single payer universal healthcare system, medical attention will not be distributed based on who can afford it, rather it will be based on who needs it. Insurance companies will no longer be able to accept or deny a patient based on how much money they stand to make.
People only believe health care is a right because they don't truly understand how much wealthier and safer we are than in most other points of history. Calling something a right is only a strategy employed by people who believe that people with money should be paying for something people without money want.