KJM7, I think that's exactly how it would probably work. In this case, it's a smidge more involved, because my Cardiologist is situated "in-between" my PCP and my surgeon. PCPs refer patients to Cardiologists, and Cardiologists refer them to Surgeons. So I don't think my PCP would be keen to refer me directly to a surgeon I'd heard good things about. And of course, everybody's used to dealing with the people and institution they're used to dealing with, quite apart from the role of Government as the Insurer. But the ultimate choices are usually the patient's, in theory and in my experience.
I've also occasionally had one specialist refer me to a "competitor" specialist (e.g., one sports-medicine clinic referred me to another, when they didn't have a spare Ortho Surgeon and I had a torn Achilles), without my having to go back to my PCP.
Like anywhere, I have more choices in Toronto than I'd have far from a big city, but I've never felt that the system that pays the bills was restricting my choices, except in relatively minor cases. Here's one: Kryptonite glue hasn't been incorporated into "the book" for sternum closure yet . (It's already approved for skull closure.) So unless I became part of a formal trial, I can't get it. Period.
In the US, even if my insurer refused to cover it, I could presumably put the extra $500-ish cost on my VISA and get glued together, even if that use of the glue were "off-label". Here, having a patient get "special treatment" because they paid extra is Beyond the Pale, a fundamental threat to the much-prized universality of the system, and illegal. (My surgeon says he's not sold on Kryptonite yet, either, but that's another issue.)
Interestingly, even though access to health care is totally universal, I'm pretty sure that wealth is still a stronger statistical determinant of life expectancy here than smoking! (Doctors, eat your hearts out!)
I'm a big fan of the Canadian system, in general, as are most of my neighbours -- though I personally wish that patients got to see the itemized bills (of the expenses we don't have to pay a nickel of). As it is, I have NO IDEA what kind of money is changing hands for treatments I hope I'm actually getting. After each of my past hospitalizations (3 non-cardiac surgeries), I usually got charged for a phone, or a pair of crutches, and that was the closest I got to seeing a full accounting.