It is irrelevant how brilliant your demonstration is: if you start with an incorrect hypothesis, your conclusion has no value.
Take Daniel Miessler article concluding free will is an illusion, also mentioned by Sam Harris. His hypothesis is that "true (free) influence on the world"—whatever that "true (free)" designation means—requires the ability to change the previous state of the world or to change the laws that govern the universe.
This is very much at odd with the common understanding of the word influence. Say you fail to see a banana peel on the curb, slip on it, and fail. Wouldn't you say that the banana peel influenced your fall? You would, as without it, most likely, you wouldn't have fallen. And I assure you that the banana peel neither changed the previous state of the world nor changed the laws that govern the universe.
Unfortunately, bending the meaning of words, or even worse, completely omitting definitions, too often plagues discussions on free will.