I think you read something which left out something; Belle's Theorem disproved "neo-realism," which is the idea that there was a classical-physics explanation, i/e, with real particles with real properties. It's the model EPR was trying to assert over the Copenhagen interpretation - and that, indeed, was its only purpose, and I find it odd that you bring that thought experiment up out of the context of its intent.

Well, actually, Everette's Many-Worlds actually repermits classical physics within its confines, and hence real particles, as do other superdimensional interpretations - within his model, you're still permitted all the trappings of classical physics. (As they break an assumption of normality in Belle's Theorem, namely, that there is only one universe, or in the case of superdimensionality, that the universe doesn't extend in other directions we can only detect abstractly.)