First, Fox gets basic facts wrong in its coverage of the story (like the role of the Office of the Public Guardian and Trustee), then posters with an agenda distort it further.
This is undoubtedly a tragic story.
The hospital may be motivated, in part, by a concern about spending medical resources in a situation of medical futility. However, by law they cannot do anything without consent. The court order gave a deadline for the parents to consent, but since the parents didn't consent, the hospital wasn't able to do anything.
I don't have the court decision in front of me, but we do have an independent judiciary. This wasn't a decision of a bureaucrat bean-counter.
If the parents don't give consent, the hospital may seek it from the Office of the Public Guardian and Trustee. No, they are not Public Defenders. They are a special government office mandated to provide specific services to people who are mentally incapable of making their own decisions - including health care decisions. In the case of a minor, the criteria for their health care decision would be simply the best interests of the child. They can't consider the cost issue.
Now, I don't pretend to know the least horrible way for a child to die. It all sounds hideous. I'm not sure, though, that it's better to subject this child to a tracheotomy just so he can be moved home, as opposed to simply removing the breathing tube. It may be - and perhaps the fact that the parents had previous experience with this gives them a reason to choose it now.
There are issues here about the extent of parental discretion in making medicals decisions, and the role of hospitals where they believe that further treatment is futile or even harmful. These issues should be discussed. Falsely labelling this as an issue about Evil Socialized Medicine, however, helps no one.