The hospital hasn’t put her in the morgue yet.
Technicalities and all that. They can declare her dead but they aren’t treating the body that way.
That is because they don’t want to give the lawyers any more ammo than they already have. Imagine how a judge issuing an injunction against taking her off the support, only to be told she’s already been sent to the morgue, would be taken by a jury in the inevitable civil proceedings surrounding her tonsillectomy.