The Schiavo case ought to be particularly disturbing to people who doubt the existence of a Supreme Being, Heaven, and Hell. If there is no life after death, then all any of us has is his or her life here on earth, making that life all the more significant and inviolable to its possessor.
Your logic is correct, but the atheists will not go that route. Rather, they have determined that since life here is all there is, it may as well be 'productive' life.
That's why the Hemlock Society, and Kervorkian as its branch, exist.