> "No physical theory of local hidden variables can ever reproduce all of the predictions of quantum mechanics."
It's more accurately phrased as, "No physical theory of local hidden variables with observations that are statistically independent can ever reproduce all of the predictions of quantum mechanics."
This is actually a new loophole that 't Hooft is exploring in his cellular automata interpretation of quantum mechanics, ie. it has local hidden variables, but because all matter shares a common history from the Big Bang, no observations we can possibly make can be statistically independent of each other.