Why not start by asking the person that now owns the place if they gave permission to the neighbor for the drainage?
It's always better to start knowing the facts, and your own statement indicates that permission has been given; i.e. aloud = allowed, and allowed = permission, either verbal, written or consent over time by lack of any contrary action.
Agree with you absolutely. If he granted permission, there is no Adverse Possession. For all you know...the tur owner might want the extra water.