Medical treatments and insurance

Recently my sister has changed her career path from working to become a doctor to wanting a different job majoring in public health. She said her reasoning behind this was because of the "politics" involved, saying that the insurance companies wouldn't cover certain medical treatments and that's something she's completely against and wouldn't want to be a part of. But in a question of what's fair and not fair based on a first come first serve basis, can one say that someone who comes first with no money should be treated rather than someone who can pay for the treatment? In an ideal world everyone would get the medical attention required to bring them back to perfect health, but this is not an ideal world. A factor which comes into play is the resources available. For example we can look at a donor list. There's only so many organs which are available to be transplanted. Of course there's already priority for donors on the list, but a patient who does not have the money to pay for the transplant but comes first should not be prioritized over another patient who does have the money to pay for the treatment, assuming that both of their situations are the same. My sister has good intent saying that everyone who needs treatment should be treated, but that's simply not viable. It's like the old "can you weigh two different lives" argument, except with money.

I'm not sure if I did this right by taking a side on the knowledge issue, my bad if that's the case.