Yeah, I understand why the author wants to turn it into a probabilistic argument, but it doesn't quite work with the circular cave analogy. You need something where the entry and the exits are different, and Mick Ali were able to use his secret to affect the outcome at the exit.
What if Mick Ali were going down one of those twisty waterslide tubes, and could say his secret phrase to shunt himself off to a different fork, so he could come out at a different tube exit at the bottom?