I'm following this story too and I'm shocked to see such cruelty. I am wondering if there's not more to this story, something bad enough they're ready to do everything to cover their tracks? It might be about vaccines or God knows what else...
Otherwise, yes, parents have to rights when it comes to their children, at least in the UK. I was just reading of another story of a little boy left to die in the same circumstances. It appears that child had been deprived of oxygen at birth, so there's no connection to the story of Alfie or Charlie Gard - but the parents have been put through the same ordeal in all cases.