  Contrary to counterfactual definiteness quantum theory teaches us that
measuring instruments are not passively reading predetermined values of
physical observables. Counterfactual definiteness allows proving Bell
inequalities. If the contextual character of quantum measurements is correctly
taken into account the proofs of these inequalities may not be done. In recent
computer simulations of idealized Bell experiment predetermined successive
outcomes of measurements for each setting and predetermined time delays of
their registrations are calculated. Time windows and time delays are used to
select various samples. Correlations, estimated using these selected samples
are consistent with the predictions of quantum theory and the time window
dependence is similar to the dependence observed in some real experiments. It
is an important example how correlations can be explained without evoking
quantum non-locality. However by using a suitable post-selection one may prove
anything. Since before the post-selection generated samples may not violate
Bell inequalities as significantly as finite samples generated using quantum
predictions thus one may not conclude that counterfactual definiteness is not
able to distinguish classical from quantum physics. Moreover we show that for
each choice of a time window there exists a contextual hidden variable
probabilistic model consistent with the post-selection procedure used by the
authors what explains why they are able to reproduce quantum predictions.
