So there was no settled "brain dead" diagnosis in that case, as in this girl's case. There is no disagreement, it seems, among different doctors that she is brain dead. There's nothing there in the head except inactive gray matter, to put it crudely.
I think the parents don't understand what "brain dead" is. They think if a machine keeps her heart pumping, that she must be alive. Her mother said as much. I saw this same thing after the O J trial, when jurors talked about the DNA and clearly didn't understand what it meant or that it was real evidence. DNA was new back then. Some people just don't understand some things. Plus, they should've been given more time than 2 weeks to let their daughter's condition sink in. It was all too sudden, I think. If the parents were paying the bill, though, that plug would've been pulled by now,IMO.