Bell-type theorems, considered as proofs of the logical need for spooky actions, in order to accommodate the predictions of quantum mechanics, have two problems. The first is that the theorems postulate a “reality” structure basically identical to that of classical statistical mechanics. Bell’s theorems then show that imposing “locality” (factorizability for fixed λ) within this classical-type reality structure is incompatible with some predictions of quantum mechanics. But that result can be regarded as merely added confirmation of the fact that quantum mechanics is logically incompatible with the conceptual structure of classical mechanics. Simply shifting to a classically conceived “statistical” level does not eliminate the strong conceptual dependence on the known-to-be-false concepts of classical physics.
The second problem is that the condition of “local realism” is implemented by a “factorization” property, described above, that goes far beyond Einstein’s demand for non-spookiness, stated above: in addition to the non-dependence of outcomes in a region upon “what is done” in the faraway region the local realism conditions entails also what Shimony calls “outcome independence”. That condition goes significantly beyond what Einstein demanded, which is merely a non-dependence of the factual reality (i.e., observed outcome) in one region on the choice of experiment performed in the faraway region. But “outcome independence” demands that the outcome in each region be independent also of the outcome in the other region.