What about the situation where the parents insist on no treatment at all in a blatantly obvious case of an illness that can be successfully cured with little or no side effects? How is the line drawn?
I'm not sure if there can be an absolute standard in the case you mentioned. It seems the only thing that can be done is to allow judges and juries to assess each individual case. The purpose of law is to balance the natural rights of individuals (including parents) and those of "society." Neither side has absolute license to do whatever they want.
As a rule, I believe there needs to be more flexibility for parents to choose whatever treatments they view as best for their children. Some, for religious reasons, might choose faith in God in place of medical treatment. This is not the same as simply not caring about their children's needs, or choosing to deny them any care. In such a case of negligence, the parents should be held liable.