I've been following this thread kind of haphazardly, but I have to come in and say that what you're saying, whether you're trying to or not, is discouraging people from posting with their ideas/thoughts on a puzzle, which I think is a key aspect of BD being a 'community' rather than just a website.
Even if people are wrong, they may say something that inspires thoughts in others, and that in itself is valuable. I am a scientist, and highly value collaboration. Pretty much all great discoveries, although often credited to one person or the other, were made by a collaboration or at least one person building the past works of others.
Also as a scientist, I've noticed that in science, economics, game theory, and even math, there are still problems 'experts' disagree on the correct approach to.
And personally, as a puzzle maker who likes to make somewhat complex puzzles, I highly encourage people to work together and share their working thoughts. It usually 'gets the thread going' and builds a kind of happy, fun atmosphere as well.
To be honest, I have not given this particular puzzle enough analysis to form an opinion on who is 'correct', my beginning line was with probabilities such as your first line, but I never took the time to finish. I recognize that you've put a lot of work and thought into your answer, and you gave a really good and thorough explanation...but I have to point out, it does not constitute a proof...your own 'comments' in red show the parts that need to be completed for it to be a proof.
Welcome to the den ;P.