Every time some dumb celebrity gets on their hobby horse about parental rights and vaccinations it contributes to situations like this. At some point, when the medical opinion is clear, the rights of the parents should take a back seat.
There needs to be a procedure to check the claimed beliefs of the child outside of the influence of the parents and the church leadership.
Last time I was in a children's hospital (with one of our kids) we ended up speaking to the consultant about this very thing - how as a kid you were brought up and coached on these situations in advance and had it ingrained how you had to respond to make it look like your own decision but what would happen to you if you let people down. They were quite surprised but seemed to recognize that it fit in with their side of experiences they had with JWs.
She'd been involved in cases where they had eventually got court orders to take it out of the parents hands and we explained that while many JW parents would protest that because they were pressured to they would be really secretly glad of it happening. She actually thanked us for explaining that - I can imagine the conflict that the medical staff must feel being told they would be doing "the equivalent of 'raping' a child" when they are simply trying to save their life and have dedicated their careers to helping sick children.
We need a network of educated and informed people who can provide guidance on what to ask and how to strip away the rehearsed and practiced answers to determine whether the beliefs are truly deeply held convictions or just a child's natural desire to please their parents.