According to one school of thought. That assertion has not been proved.
Some first class scientists and thinkers have examined the empirical evidence and come to a different conclusion. Nobel prize-winning neurophysiologist Sir John C. Eccles and the eminent philosopher Sir Karl Popper were perhaps the two best known of those men and women who have looked at the evidence and concluded the dualist-interactionist model is a much better fit.
The eminent neurosurgeon Wilder Penfield came to a similar conclusion based on hundreds if not thousands of experiments carried out on conscious epilepsy patients whose exposed brains he electrically stimulated.
Now, you may disagree with Eccles, Popper, and Penfield. But your disagreement does not mean their views are unsubstantiated or irrelevant.
In any event, the dualist-interactionist model does not serve to exonerate Greer, Schiavio, Felos et al, or to justify the forced starvation and dehydration of Terri Schiavo. Many murderers have sought to rationalize their deed by appealing to their own sense that the victim was better off dead. But that's all it is--a cynical and desperate rationalization.
Be that as it may, Terri was the one who made the decision -- Judge Greer merely confirmed it.