Wait, in the US doctors have the right to not treat a patient?
That's actually insane. Whatever happened to the Hippocratic Oath?
No. Please stop getting your information from manga.
In America, doctors that are capable of rendering aid have a duty to treat. It's basic medical ethics. Also, the treatment WILL be rendered regardless of the patient's ability to pay (I know rest of the world want to think that people with life threatening injuries are just turned away because their credit card was declined, but that does not happen and would be illegal if it did; any hospital that did that would get sued into oblivion as well). See: Emergency Medical Treatment and Active Labor Act.
There are limitations to this, however. For instance, a pathologist is a medical doctor, but they are not expected nor realistically capable of offering emergency medical care like trauma surgery (and if they tried doing so, which they shouldn't, and something goes wrong they can get into legal hot water for doing so). Also, if it's clear that the medical aid would be meaningless and would not actually help or save the patient, they are not required to do so.
The only thing after that is asking a doctor to do something that is not medically required. There's actually people that WANT to have their perfectly healthy limbs removed for... whatever bizarre reason... and find (quite rightfully) that very few doctors are willing to remove a perfectly healthy and useful limb just because the person wants to and view it as doing harm and thus be a violation of the Hippocratic Oath, even if the patient wants it for whatever reason. The doctor in question here has no duty nor obligation to do so and will quite reasonably decline to do it.