^But the American system has the same limitations on treatment -- if not more, and they're imposed by the insurance companies. You certainly can't get any treatment you want here. And just like Americans can do, if someone in a country with socialized health care wants something that is not provided, they can pay for it privately.
Actually, some restrictions are simply because it's good medicine. We don't give antibiotics for a viral infection anymore. They're worthless for the illness & cause more problems down the road.
And, yes, there are lists for organ transplant. Patients undergo screening to determine if they can handle the follow-up necessary. We're not going to give a new liver to someone who won't quit drinking. If someone can't be compliant with a medication regimen, they're not going to get a new kidney.
An MRI is not the first diagnostic test offered if you have a headache.
And no amount of begging, pleading or offering money is going to get you those things if they aren't medically necessary.
My point is (and this is from 30 years in healthcare administration): All healthcare is rationed. It's not an infinite resource.
In the US, we ration largely on a person's ability to pay for care--and I find that an immoral way of doing things.