What is Single-PayerNate Silver is almost right here.
It is true that we do have a single-payer system with some possible private provisioning (but provisioning is mixed, as I have had care at the local hospital, publicly owned, while I am sure my cataract surgery was done by a private clinic, using facilities that might have been in a publicly owned hospital). And it is true that this is not like the NHS, though the UK apparently has a private domain that is an alternative not generally available in Canada.
And here there are many restrictions on private provisioning, driven largely by political arguments that deliberately try to exploit the confusion Nate is describing.
Of course the reality is even crazier, as we actually have a number of governments involved (Canada is also a federation), and of course what is not deemed medically necessary is in the private domain. So sometimes you can pray that you are suffering form a problem the government does not think needs to be treated, as then you can actually get private care.
It is proving to be very entertaining watching Obamacare trying to take shape, and I would say the last month has been one of the most engaging times to be reading economics blogs, just for all the interpretation and struggle to identify and avoid the mistakes other countries have made in shaping their healthcare systems (and, concomitantly, trying to figure out how the healthcare systems in the other countries work - I sure don't understand mine).