One of the reports says that she'd begun eating and drinking again just a few days before her death. Two days before her death, parents ring up GP expressing concern but say she is now ingesting again, the doctor prescribes build up drinks so that she can put back on the weight she lost (though theres no evidence that the parents weighed her so probably just said to the doctor that she's lost a bit of weight, rather than two stone).
Sometimes kids don't eat, so the psychologist was there to deal with that. But did she really know the severity of the problem? She was neither a doctor nor a nutritionist and could not be expected to know any better than to reassure the worried parents before their appointment the next week. Eventually perhaps she would have sorted out the childs phobia.
The hospital refused re-admission? Well heres a thought, there was nothing medically wrong with the child. This was a job for the psychologist, who as they knew they were due to see in a matter of days.
So who was responsible for keeping her healthy and well until the psychologists visit? The parents. All the health professionals above never saw her, so could not have known. As far as I'm concerned that is the parents fault, for not putting her in the car and driving her to the hospital/GP wherever. Any health professional who recieved a phone call from them saying that the child had lost weight (but don't know how much) and had only just starting eating could have checked and seen that she had an upcoming appointment with a psychologist, and told them to wait. From the sounds of it the parents only even bothered to pick up the phone in the few days preceding her death.