Yes, all this is true, but I think you're still missing the point I'm trying to make. Classical mechanics succumbs to statistics without any compromises in terms of being able to make reliable predictions using a TM. But quantum mechanics is fundamentally different in that it produces macroscopic phenomena -- the results of quantum measurements -- that a TM cannot reproduce. At the most fundamental level, you can always make a copy of the state of a TM, and so you can always predict what a given TM is going to do by making such a copy and running that instead of the original TM. You can't make a copy of a quantum state, and so it is fundamentally impossible to predict the outcome of a quantum measurement. So a TM cannot generate a random outcome, but a quantum measurement can.