The parents do not have the legal right to harm their child, period. Refusing to have the child treated is morally the same as refusing to feed the child and thus is an act of harm. To my knowledge, no court has ever sided with the parents in such a case.
BTW, evidence-based medicine means that the treatment has been tested in large-scale studies and determined to be equal to or better than other existing treatments for the same condition. Physicians are trained to practice evidence-based medicine. As far as I know, there has never been a study where a proposed treatment was euthanasia—such a study cannot exist, since euthanasia would lead to a worse outcome (faster death) than any existing treatment or no treatment.
Is the treatment 100% guaranteed? 80%? 50%? Can anyone ever really know? Who says “when”? Would you advocate this girl be forcibly removed from her parents’ home so that she gets “approved” treatment? Is natural death ever acceptable?
Obviously on some level I’m playing devil’s advocate here, but I think it’s an issue conservatives should be concerned about — now more than ever. At what point IS it a parent’s right to overrule “their betters” when it comes to their children? Because the same arguments I’ve read here could apply to everything from outlawing homeschooling to removing children from “superstitous” (i.e. religious) homes.