Correct me if I am wrong, but to me it seems that the major catalyst behind all of this was the original doctor making direct threats against the parents like some kind of common thug.
The parents were terrified of the prescribed after-treatment, and with good reason. The hospital wanted to pelt the boy with radiation that could very well have destroyed the rest of his brain and turned him into a permanent vegetable. What parent wouldn't be hesitant?
But when the parents say "Hey, we don't want to go this route. Let us try this instead," and the doctor replies "No, your son WILL get this treatment and you will go along with it or else I will get the court to take away your custody," what are they really supposed to do as parents?
The boy is on death's door anyways and his future standard of living looks grim no matter what. Ethically you allow the parents to try the alternatives that they want. But the doctor was stubborn, and because of his stubbornness he spooked the parents and caused them to flee (justifiably so I'd say).
I also want to point out that the parents did not sneak the boy out of the facility. They took him on a pre-scheduled outing that was approved by the hospital. The hospital expected him to be back in a few hours, but the parents simply didn't come back at all.