It is shown that the before-before (or Suarez-Scarani) experiment refutes hidden variable models with a deterministic (“realistic”) nonlocal part, whereas experiments violating Leggett-type inequalities refute models with biased random local part. Therefore the claim that Gröblacher et al. (Nature 446:871–875, 2007) present “an experimental test of nonlocal realism” is misleading, and Marek Żukowski’s (Found. Phys. 38:1070, 2008) comment misses the point. A new experiment is suggested.

Leggett formulated an inequality that seems to generalize the Bell theorem to non-local hidden variable theories. Leggett inequality is violated by quantum mechanics, as was confirmed by experiment. However, a careful analysis reveals that the theory applies to a class of local theory. Contrary to what happens in the derivation of Bell inequality, it is not necessary to make the hypothesis of outcome independence to derive the Leggett inequality.