Not even the government or the police. Hence why I am against the death penalty. If a doctor nurses a serial killer to health they should not be judged. Though I disagree with the statement "a doctor's job is not to decide who is morally worthy of care and who is not". Morality is not a set of rules. It derives from the individual. In the end, The doctor cannot be forced to do their job on this specific case or not to. If they think it's right they should be let to do so. If they think it's not then let them not be forced.
A doctors responsibility is to treat patients. Not to decide who is morally worthy of care and who is not. Plus, You cannot get information from a dead or incapacitated individual. If the doctor allows them to die, That may put a strain on an investigation. A doctor has no right to decides who lives or dies anymore than the killer does.
Those who once broke other's the inviolable right to life are not worthy of it.
Also, The money, The attention, The work that the cure demands for the criminal can be used to another urgent patient who worths it more.
These are the reasons why I believe doctors should not treat serial killers in an urgent state.