Don't you wonder what HKS was doing during that time? From what we've been able to tell, he had no other clients.
and if she had a nurse and a 105 temperature why was the nurse helping Stern boat shop? Why wasn't she at the patient's side? Why at 105 temp didn't they call an ambulance instead of icing her in the tub?
Worse, the "nurse" was boat shopping, yet the Dutch companion of King Gibson claimed it was she who noticed something was wrong and told the nurse.
Incompetent comes to mind, but also a whole lot of deception. If this was Murder She Wrote I'd say they wanted an alibi while she was dying to give all of them cover.