It wasn't a case of emergency surgery needed (I have done my research, you know). Under a nationalized system, we would have been triaged as 'not going to die right now' and scheduled when the doctors could get to it. Because our healthcare system allows us to control appointment times, we shopped around, got better doctors and found a schedule opening. It turned out the problem was way worse than the doctors had realized, and it was a very good thing we had pushed. Not being able to control doctors and scheduling would have left us in a much, much worse position.
That's about as valid a criticism as saying that with privatised healthcare doctors will leave you to die if you can't pay the exorbitant prices. Nationalised healthcare doesn't have to completely ignore the concerns of citizens, and privatised healthcare doesn't have to be entirely staffed with dicks.
EDIT: Wait how did a healthcare discussion end up in this thread?
To my understanding, people being left to die because they can't die is pretty much a myth even with the current US system.
Anyhow, living in Canada, I can say that it is true that if you urgently need care you'll pretty much get it immediately, and there aren't "death panels" in the sense some Americans say. However, this sorta disguises some problems with our current system. For one thing, if you have a very painful/debilitating issue and it's not life threatening, there isn't a guarantee that you'll get treatment in any reasonable amount of time. So someone spends 6-8 hours in the waiting room in pain, maybe sees the doctor, and then either the problem has a simple solution that could have been done earlier or something is scheduled in the future.
The other problem, which is the one Ghillis is talking about, is that you can see a doctor for a problem, it turns out to be
potentially fatal in the long term so another appointment/surgery is scheduled for the future whereupon it turns out that things worsened for one reason or another and the planned surgery won't work anymore. This problem can stem from many issues: some specialized equipment is fairly rare (at least compared to the US), and thus is either not used much or else has very long wait times to use. Doctors don't want to push non-emergency issues forward too fast, since enough doctors doing that results in problems (eg. on more than one occasion there have been ambulances driving all over Toronto, unable to find emergency rooms with space). Finally, you might simply have shitty luck and get complications the doctor didn't foresee in between checkups. Regardless, it's a bit more complicated than "get your healthcare early if you need it, otherwise wait a bit".
On the topic of the US in rankings, there are two things worth noting: first, the UK, unlike countries like Canada, has both private and public systems. From what I've been told, the NHS's quality varies wildly from one area to the next ranging anywhere from "pretty good" to "abysmal", so if you want anything reliably good you basically have to pay twice. Also, both countries feature systems that vary in quality from one hospital to the next, with the US notably having some of the best hospitals in the developed world as well as some pretty terrible ones. I'm a bit skeptical that the survey is entirely representative, though, simply because I know for a fact that, at least near where I live (Windsor, across from Detroit), waiting times in the US compared to Canada are basically non-existent.
Anyhow, I'd say that, for most people, healthcare quality isn't too different for people from Canada, the US, or Europe, and I'd agree that it's mostly just "different". I mean, the biggest problem in the US is the cost, but to my understanding most Americans receive insurance from their employers at basically no cost (even before the ACA), and the care they receive is quite good generally speaking. It has a lot of problems, mind, but this isn't really the place to get into a long winded discussion of the problems of the American healthcare system.