There's a
huge middle ground between reducing cognition to statistics (as you seem to be proposing) and "abstracting away" the statistics. You seem to be accusing any approach that's not "statistics all the way down" of ignoring the statistical nature of the mind. When in fact, there are many approaches to cognition which make heavy uses of advances in statistical theory without reducing cognition to statistics.
What you're proposing is an overly reductionist ontology, IMO, and yet I agree that statistics are important, if not critical. (Hint: not the boring linear kind of statistics that you so often see in Big Data)