I do not understand why anyone would think that the child would be better off by staying "alive", even if the treatment proved to be successful (which most likely wouldn't be).
If by some miracle the experimental treatment worked (which even the American doctor says is unlikely); he would not die due to the illness, but his muscles and brain would still remain permanently damaged. He would be blind (eye muscles too weak according to the hospital), deaf, unable to move, forever stuck in a bed, needing machines to breath, unable to feed himself, to clean himself, to speak, or to laugh, to play with friends, to go to school, to form his own family, to live a fulfilling life, probably unable to move and depending how much degeneration his brain suffered, he would be basically a vegetable. He would be alive but it would be as if he wasn't, he would not be able to do anything. Remember: he has suffered extensive muscle and brain degeneration.
Is that life? That's basically being dead alive. Would anyone really say that this situation is is any way preferable to death?
It is almost monstrous to let him live further, maybe in pain, unable to know what is happening to him. His whole existence has been pain and suffering so far, and will continue to be so if he is kept alive artificially.
I know emotions get in the way, but the parents should know better.