As part of the way the NHS functions, authority for acceptable and ethical treatment is given to a patient's medical staff. This is necessary to prevent parents or other medical lay-people from refusing necessary treatment, implementing alternative remedies rather than doctor prescribed ones, or any other ways in which a legal guardian could negatively impact treatment. For instance, if a child was in the hospital with a life-threatening infection, the NHS could prevent the parents from visiting him and giving him an unknown family remedy because that would be materially likely to harm the patient.
And as sad as it is, part of acceptable and ethical medical treatment is preventing patients from experiencing undue suffering or hardship in end-of-life situations, which can include refusing transfers and/or a controlled removal of life support for patients who are essentially guaranteed to die. It is not ethical for a doctor to recommend aggressive action they believe has an insignificant chance of working just because its something different and miracles can happen; the most likely result of such recommendations would just be for those patients to suffer before dying.
Based on the article you have linked, the parents wish to transfer Alfie to a hospital in Italy, but even there they expect to simply perform palliative care; in this situation, that would essentially be putting Alfie on life support and hoping for the best. Even with Alfie's success at breathing on his own, neither the hospital in the UK or in Italy believes there is any chance Alfie will recover and can only plan to keep Alfie alive as long as possible. Given this situation, the medically ethical decision is not to keep Alfie alive but vegetative forever, nor would it be ethical for doctors to recommend a risky transfer to another country just so they could keep Alfie alive but vegetative.
