Not all entangled states violate Leggett's crypto-nonlocality

This note is a reply to M. Navascu\'es' claim that "all entangled states violate Leggett's crypto-nonlocality" [arXiv:1303.5124v2]. I argue that such a conclusion can only be reached if one introduces additional assumptions that further restrict Leggett's notion of "crypto-nonlocality". If a contrario one sticks only to Leggett's original axioms, there exist entangled states whose correlations are always compatible with Leggett's 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 Bell's assumption of local causality.
Comment: 3.5 pages. v2: typo corrected. Published version (titled "Bell's local causality, Leggett's crypto-nonlocality and quantum separability are genuinely different concepts") concentrates on clarifying the differences between these 3 notions, rather than on the claims of arXiv:1303.5124v2 (which has since been updated)