The following extract from JW.org's website might throw a little light on the way the parents were thinking:
A Witness will view the making of each decision as if he were a driver approaching a busy intersection. If he just followed the cars ahead and sped through the intersection, he could cause serious damage. A wise driver will slow down and evaluate the flow of traffic before proceeding. Likewise, Witnesses do not rush into making medical decisions, nor do they blindly follow popular opinion. Instead, they weigh their options and examine Bible principles before making a decision