Not all entangled states violate Leggetts crypto-nonlocality

This note is a reply to M. Navascues claim that all entangled states violate Leggetts crypto-nonlocality [arXiv:1303.5124v2]. I argue that such a conclusion can only be reached if one introduces additional assumptions that further restrict Leggetts notion of crypto-nonlocality. If a contrario one sticks only to Leggetts original axioms, there exist entangled states whose correlations are always compatible with Leggetts crypto-nonlocality---which is thus a genuinely different concept from quantum separability. I clarify in this note the relation between these two notions, together also with Bells assumption of local causality.