I don't really know what systems the Brits and the Maples have, but over here I think anyone can get specialist treatment of sorts under the public health system, but the waiting lists are so long you might be dead first. Having private health insurance allows you to jump the queue and pick and chose services/doctors more - i think.

Happy to be corrected by someone who actually knows tho I am fortunate enough so far not to have had much other than basic dealings with the medical system....touch wood.