I have never heard of that of koryu generally. I could see it being a Daito ryu thing to go along with the factionalism and the inherited pathos of Aizu culture. But whatever, it's private knowledge. So that leads us to here, where we cannot stop wrestling with this material on the internet, but nobody can openly talk about where it comes from.
Well my recollection is from about 8 years ago now, I briefly trained in one of the older Koryu with a Menkyo holder here outside Seattle. That's what I remember being told by him, but I could be wrong about that. I have no experience or abilities really to speak of.
All the best to you and your Budo path.