It was never called Ueshiba-ha Daito-ryu. Ueshiba called what he did Daito-ryu and issued makimono in that name. After the break with Takeda, Aikibudo (there was a brief period where he referred to his art as Kobu(something), linking to the Emperor. I do not believe he ever had a dojo of Aioi-ryu. Rather, he used the term to refer, after-the-fact, to a period of his own training (and not explicitly - he would say something like, "I studied Kashima-ryu, Yagyu-ryu Aioi-ryu . . . .Given he took whatever he saw and per Sugino, then would say, "In Aiki, we do that this way . . ." - I don't think he made much distinction between what he 'stole' and what were his own changed slants on Daito-ryu.
And there was, to my knowledge, no Daito-ryu enrolled in the Butokukai.