* Your last remarks suggest you haven't read those Werner refs and don't know what is meant by the term "classical" as I've used it here - it's a reference to the structure of (general) probability state spaces, not to classical physics per se - and you should substitute "(naively) realist" for "classical" in the above.
% And those familiar with the probability theoretic aspects (see my links in a comment in a different thread here, or Tom Banks's teaser: http://blogs.discovermagazine.com/cosmicvariance/files/2011/... ), probably won't want to do that. For example, the reason violations of Bell-type inequalities occur in QM is mundane from this perspective: "What on earth did you expect?! You have observables that don't commute! Use the appropriate inequality." https://sci-hub.tw/10.1016/0375-9601(87)90075-2