All I can say is that my heart goes out to those parents and I truly hope they find the right treatment for their little boy and that there can be true cooperation between them and the medical people. They just seem like a loving, caring family trying to do the best for their child. Doctors don't always know what's best, even if they think they do.
I've had my own issues with the medical profession, did my own research. Found an alternative treatment fortunately still on the NHS. They tried to talk me out of it but I went ahead and went to another county for the treatment. It was highly successful and meant I didn't end up having needless surgery.
If this family want to fund private treatment in another country for their son then why shouldn't they be allowed to do so?