Nonlocal determinism implies local indeterminism.
In a universe which evolves nonlocally, a localized observor does not have access to enough information to correctly predict his deterministic evolution. This ignorance will lead to local laws which are probabilistic due to the ignorance of the nonlocal information. In such a universe there are two mysteries: (1) why no signaling? and (2) why quantum theory is a good description of the probabilities arising from the ignorance of nonlocal information? Further, this interpretation amounts to an untestable hypothesis, unless the answers to (1) and (2) are not exact.
Dave, is there a more detailed version of this idea somewhere? I am not a physicist but find this very fascinating. Did Einstein think along these lines?