Technically, even then it only rules out efficient local hidden variable theories. A theory where every particle carries a local hidden variable containing the entire state of the universe can (obviously?) emulate any other theory, quantum or otherwise (with a bit of finangling for things like quantum field wierdness).
Yes, you're correct. However, nonlocal hidden theories bring other issues that don't seem plausible. That's why the best current quantum field theories do make radiation a purely random event. None use nonlocal hidden variables.
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