@Finn dAbuzz,
I am not claiming that there is a contradiction in your position, but I want to point out that you are accepting that there are cases where it is appropriate for the State to be involved.
So, this becomes a question of medical ethics. Your position is based on what you are calling the "sanctity of life".
Medical ethics don't mandate that you keep some one alive at all costs. I am not sure what "sanctity of life" means, but it shouldn't mean refusing to accept the fact that people (including children) die.
My position on this case is that questions on medical ethics should be made by the medical establishment. The parents obviously have a very strong interest, and they should a voice... but the parents aren't in the position to make a rational decision on the most ethical course of action, or what is medically in the best interest of the child.
There are many cases where medical ethics means letting critically ill people die. There was an interesting story about lives that could be saved by allowing people to sell organs... we as a society have decided that this practice, even though it would save lives, would cause serious ethical problems and opportunities for abuse.
Not knowing the specifics, I think I tend to side with the doctors.