They were always going to pay for it themselves.
The issue isn't money.
MW says "This sort of thing is not the job of government-appointed arbitrators" but it is, in the UK.
The issue is that the law says the state gets to decide what is in the "child's best interests".
Adults are allowed to make stupid decisions (if they are deemed competent, at least) but parents are not allowed to make stupid decisions on behalf of their children.
The doctors at the hospital felt that the parents spending the funds they raised on their own, to take him to the US for a treatment that basically isn't going to do anything beyond prolonging his life by a few weeks, is a stupid decision that is "not in the child's best interests". Frankly, I agree that it is a stupid decision.
In many countries (I don't know specifics) the doctors would say to the parents, it is a stupid idea to go to the US, but you can do what you like with your own children.
In the UK, the doctors would have explained to the parents why it is a stupid idea, but since the parents seem to be missing the bigger picture and disagreed, then the doctors said, right, we will go to court and let them decide what is in the "child's best interests".