The experts in the type of condition he has, the whole reason his parents wanted to take him from one world class hospital all the way to another world class hospital was so he could be treated by the best doctors in the field (while the staff at GOSH are marvelous they are not really trained/equipped for the type of condition Charlie has nor have they encountered it's type much before).
But nobody has really, as far as I'm aware - there are less than 100 recorded cases,
It also hasn't been demonstrated at any point, that the treatment being offered has worked on a case like Charlie's - even the doctors offering the treatment admitted this.
It's important to remember that the American philosophy of healthcare is vastly different to our own, rather than simply accept the inevitable course of nature - American doctors are far more likely to try and defy reality, by throwing endless treatments at a lost cause - often leaving patients more wrecked than they were before for no real useful outcome, or quality of life - other than maybe some useful data.