Where is the basis for saying that in this case the people who must be accepted as representing the child's interests are the medical authorities rather then the parents?
So far as I can see they have not sought to produce any compelling evidence that Alfie is suffering in a way that might justify this shift of responsibility from the parents to the authorities. They appear to be speculating beyond their field of competence, in the absence of evidence.

It would appear that medical professions with quite as much expert knowledge are ready to continue his care, in another hospital. Transferring him from one hospital here to another equally competent hospital at the request of the parents should be perfectly acceptable. Why should the fact that the other hospital is in Italy be a reason to dig in and oppose the transfer?