A cottonmouth wants nothing to do with people, and as far as the chasing stories go those are nothing more than myths. If someone is standing in between the snake, and where that snake wants to go, then it would likely move towards them, but that does not mean that the snake is chasing that person.
I know an older gentleman who lives in south Georgia and he has caught pit vipers for over 50 years. He sold some snakes to the Ross Allen reptile Institute back in the 1970s. He has as much experience with water moccasins as anyone walking this planet, and he is adamant that they do not chase people. He will go a step further and state that they are the pit viper that is probably least likely to bite a human. His experience is backed up by numerous herpetologists, who have published on this topic.