River cauvery has been flowing for centuries now along its course and the civilization has depended on it for generations. It is not fair to claim ownership on it based on its starting points and ending points now. Who knows, an ancestor of persons living on upper basin now would have benefited from Cauvery's lower basin in the past & vice versa.
Scriptures say that a river may change its course once in thousand years. Let us not make it happen faster by playing with environmental stability.
Give nature its due respect and share its fruit amicably.