Under the Australian system the government can't say "no". The government has no say in the specific medical treatment you do or do not get. It's not like the private insurance system.
Americans are so fixated on the private insurance driven, for-profit system that I think it's become impossible for them to think outside that system and conceive of better alternatives.
OB
As far as thinking outside the system, that depends, as I said things are changing.
If you have good health insurance through your employer, and you get really sick, the medical care you will receive is top notch. Anything other than that, and quality of care will start to slip, Even our Medicare System that covers elderly, and disabled is not cheap, and it only pays 80%, the other 20% is your responsibility. This simply means you have to have a supplemental plan that will cover the 20%, or, you have to find a Dr. and/or hospital that will accept what Medicare pays, and there are a good number around that will do this. However, if all else fails you have to dip into your saving to pay it, or make other arrangements, and Medicare reimbursement is pitifully low.
I am fortunate, and I am thankful, and I am humble, because I retired from the US Navy, and the Department of Defense takes care of my, and my wife's healthcare, we do have small copays, and premiums. The system is cumbersome, and like any Government program you have to deal with several layers of bureaucracy...But I'm thankful.
I still think we are another generation away from any meaningful changes to our healthcare system, with the exception of improvements to the Affordable Care Act, which will not be earth shattering, IMHO.
Generation X, my kids Generation were also pushing a National Health System, along with other social changes, but by the time they reached 30, their was significant changes in how they thought about these things, and the majority have backed away from radical changes to our society.
The US just has cultural feelings about interaction with the Government, either it's something to be viewed with suspicion, or, it's the answer to all our problems, and there are few in the middle.
This suspicious view of the Government still pervades American culture, which is why the approval rating for Congress usually sits in the 20% range, sometimes much lower. The only Government institution that is consistently receiving high public approval, usually in the 70% (+) range is the US Military.
Our Federal Government is essentially non functioning, and has been that way for many years, we have not had a budget passed in like 10 years. The US is so deeply divided, more so than at anytime since Vietnam, and until we have a functioning Government, and heal divisions, things like National Healthcare, and other needed social programs will never come to pass.
65% of Americans have excellent Health Insurance, the rest have crap, outrageous premiums, deductibles, and copays, or, nothing at all. Those who are in the 65% do not generally want big changes in our healthcare system,and are vocal about it.
But it's the "I don't trust of the Government" that's hampering any significant changes to our system of healthcare.