What I am stating is a step above church-turing, that the constituents of any physical process is either deterministic or random, computability aside.

From a purely practical standpoint, we don't know of any non-computable physical systems and it's just so painfully god-of-the-gaps to say "The brain could contain new physics that transcends everything we know even though this has never proved true with any other complex system we ever gained knowledge about. It's all proved computable".