[lclemente]

I think the problem with your analogy is that it doesn't include the measurement basis. Consider polarization of a photon: you can either distinguish between horizontal or vertical polarization with a measurement, so your basis looks like a "+". Or you can distinguish between diagonal polarizaitons, so your basis looks like an "X".

Now, considering two photons, you don't know which basis Alice or Bob will choose in advance. If you just say "the photon is polarized horizontally", then their outcomes will be random if they measure in the "X" basis. If you include so-called "hidden variables" for all possible measurements, then you're basically at Einstein's idea.

(I've simplified some things above, so please don't quote me on it ;)