We have family members whose minor child required major surgery. It was actually the JW Hospital Liaison rep that told the parents to just state that they could not approve a transfusion in good conscience as this would result in the hospital seeking the judge's order to transfuse if necessary. In this manner, they could maintain a clean conscience before God (and most of all the Cong Elders) and the doctors and judges would be the ones accountable to God.
Simple way out. No death for blood loss. No "stealing" child from hospital. No bad media publicity.