It's very sad for the parents, it must be truly awful to have such an unwell baby and I can't imagine the pain of losing a child.
That said, I think they are now being unreasonable. Well, I think their demands were unreasonable some time ago but this is a step too far. They are now blaming GOSH for delaying treatment which would have made him well again. The treatment was never going to make their little boy "healthy". It never promised to cure him, it was suggested it might provide a tiny chance of a slight improvement. It was essentially an experiment as had not been used on humans (or animals) with the same illness as Charlie. It had only be used on those with a related illness.
I can understand the parents grasping at anything and everything, but at some point reality has to kick in AND the child's best interests have to be put first. Let's be clear, my understanding is that this little boy cannot hear, see, move, swallow, communicate. He cannot breath without a ventilator. Medical experts believe he is able to suffer and feel pain, and moreover that he is suffering now (although parents disagree with this- based on "we would know"). Even a tiny improvement was not going to make him "healthy" and so is not, in my view, in his best interests.
I think the parents are projecting their anger and hurt onto GOSH and the staff there. But lets remember that it wasn't just one Dr or even one medical team who decided this. Opinions were sought from other experts, including other specialists in the UK and teams in Spain. There may well have been others. Then it was taken all the way through the courts- with unanimous agreement from all courts right the way through to the ECHR.
I think they have been badly advised, used and egged on by various individuals and groups who had their own agendas (Trump, the vatican to name but a few) and a whipped up media frenzy.
I hope Charlie's parents eventually find some peace.