Where exactly does he claim that? He knows the shouts that the Greybeards do, for sure, but I missed the conversation that leads to such a claim.
How would he know the shout Duurnehviir, or the shout that he uses to summon undead from the soul cairn? Him being able to heal any wound with the shout Alduin uses to restore dragons, or the shout that Miraak uses to reap dragon souls (and its made clear that the dragon aspect is the one that he made himself) would also be things of major importance.
Knowing the words isn't exactly understanding their meaning, or combination. Else all dragons would know all shouts, and "dragons have fire or ice breath, but never both" wouldn't hold.