Actually, that's true since death is usually deefind as the point at which all electrical activity in the brain stops, which is usually due to lack of oxygen in the brain. Many causes of death such as disease, poisoning, or traumatic injury do not directly deprive the brain of oxygen, but either a) interferes with cellular respiration, b) damages cells in such a way that they can't function properly, or c) overloads the body with byproducts of dead and damaged cells, which in turn do a) or b).