  A hidden variable model reproducing the quantum mechanical probabilities for
a spin singlet is presented. The model violates only the hypothesis of
independence of the distribution for the hidden variables from the detectors
settings and vice versa (Measurement Independence). It otherwise satisfies the
hypotheses of Setting Independence, Outcome Independence -- made in the
derivation of Bell inequality -- and that of compliance with Malus's Law --
made in the derivation of Leggett inequality. It is shown that the violation of
the Measurement Independence hypothesis may be explained alternatively by
assuming a non-local influence of the detectors settings on the hidden
variables, or by taking the hidden variable to influence the choice of settings
(limitation of free will), or finally by purporting a conspiracy. It is
demonstrated that the last two cases admit a realization through existing local
classical resources.
