Not to put an even finer point on it than already exists, but I think I'm correct in saying that hair, at least beyond the root, is "dead" tissue, which is why it may be cut without causing any pain to the person on whom it grows.
Seen that way, it's really not part of the living body anymore. The same could be said of a thick callus on the hand or foot, which is just sitting there dead, waiting to be sloughed off in time. Though it's the height of pedantry to speculate on it, if water were applied to a callus and just to the callus, it seems even more highly doubtful that it would be valid, than if it were applied (for instance) to a hand or finger.