Even with the advances in modern medicine pennyh47 there still comes a time when you have to say "enough".
I wonder whether Charlie's parents have really thought through all the implications. Think of the organisation required to transport a baby on life support across the Atlantic, and the number of people it would involve. Suppose they take him to America and he dies on the way? Suppose he dies far away in an American hospital instead of peacefully, here, with all his family around? Even if he got some benefit from the treatment I can't imagine an enormous improvement. It's not like magically shrinking a tumour.
In the end I think I would rather spend time with Charlie, taking photographs and building memories and letting him pass peacefully.