Lots of thoughtful comments on this thread.
My first thought is that it isn't simply the courts that decide what happens; it's the courts informed by medical experts.
As you say, this must be every parents' worst nightmare, and I cannot comprehend what they are going through. At the same time, I find myself thinking this is why they should not have the final decision: who could possibly make a rational decision in those circumstances? Although I don't blame them in the least for this, I suspect they are now acting more in their own interests (i.e. convincing themselves they've done everything) rather than in Archie's, even if they don't see it like this. I'm not accusing them of being selfish: their mental health is important too and, for their well-being, I do see a point in going through this process, but I can't believe it's in Archie's best interest.
"Naturally" is an odd way of viewing it; his body is only alive now due to artificial intervention. I don't want to comment on details of an individual case without first hand knowledge, but we can ventilate a body by pumping air in and out of the lungs; we can provide all the nutrition needs intravenously, and we can make the heart beat artificially through a number of pacing devices. None of this is natural. The ventilation in particular can often be mistaken by relatives for the patient trying to breath themselves. Ultimately, the chance for a "natural" death ended with the attempt to save his life.
As has been said, it's a horribly difficult situation. I do feel the courts have made the correct decision. However, his parents do need to feel they've done all they can too.