Shadowplay's answer is good but the "any kind of privately purchased insurance" is wrong. We do have private insurance in Canada either bought personally or through an employer. This doesn't functionally change the process of receiving healthcare; if you are a new patient and you're unable to provide consent for record transfer or to confirm the insurance details, you'll be covered by the provincial plan until you can remedy that.
A single-payer healthcare system guarantees a minimal level of care for every individual within your borders, aka universal healthcare. Knowing America, though, they'd probably find a way to make it optional or a cash cow because they aren't willing to set regulation and conditions on a federal healthcare system. In Canada we have federal mandates but provinces are left largely alone when it comes to having the system come to fruition. Ontario, for example, funds and controls its healthcare system through taxes. Here in BC you pay a monthly/yearly fee. The end result is the same but the route can be different.