I don't follow. Quantum mechanics means that physics is stochastic, and only approximates classical determinism in aggregate. Meanwhile, brains seem to operate in a critical state that can be tipped to different phase transitions by small perturbations, so there is potential for a quantum event to influence the brain as a whole in a nondeterministic fashion.
This means that strict physicalism still leaves the door open to our behavior being stochastic rather than deterministic, doesn't it?