Proven, no. But our current best theory after 100 yeasts says “yes, it seems dice is played.” It’s the deterministic curmudgeons who keep trying to find a way to ignore that!
All that's proven is that statistical models are a good fit for something we don't really understand. No different than using epicycles to solve the problem of planetary motion.
You're wrong and and so was he and you definitely shouldn't weigh in since I'm sure you're not nearly as qualified as he was (neither wrt physics nor virology):