Public/private boundaries in Canadian healthcare: some clarification

Most Canadians think that "medicare"/our healthcare system (for the differentiation is certainly not clear) is "public," meaning universal and pre-paid by their taxes. Those who have heard of the five conditions of the Canada Health Act (CHA), or at least the phrase, "public administration," are doubly confirmed in their belief. It comes as a surprise to concerned citizens to learn that, to get federal funding, a province has to set up a "single payer" for health services to fall under medicare, that is, hospitals and physicians. Then, if more information is introduced to distinguish between funding and delivery of services, and it is stated how the former is public, while the latter is mainly private, the audience starts challenging the speaker. Explaining that the delivery of services is private because doctors or nurses are not civil servants, for example, comes across as one more great Canadian fiction. "After all, they are fully remunerated by public funds--my taxes." All of this to recognize that, in Canada, discussions around the public/private divide, from whatever angle, are surrounded by preconceived, often common-sense, ideas rejected mainly by students of healthcare systems.