No paradox if Pinochio doesn't know the nature of how the paradox works himself, and therefore cannot be said to be telling a conscious lie.
And then there's the classic Grandfather Paradox. No, not the time travel one, the one where your grandfather's house smells like pipe tobacco but your grandfather doesn't smoke pipe tobacco.
Yeah, the classic Grandfather paradox only holds up in a single line universe. The Grandfather Paradox doesn't hold up in geometries that allow for a multiverse.