(I seem to recall Ellis relating a Sho Chiku Bai - Shinkage - Hikitsuchi connection.)
Now that I think about it I recall Takeda giving Ueshiba a Shinkage Menkyo [with no evidence of any Shinkage Ryu teaching, so some hypothesize this was an official "nod" without necessarily having any specific Shinkage linkage] I wonder if there could be a Sho Chiku Bai relationship to that?
Perhaps O-sensei identified his Kenpo as Sho Chiku Bai no Kenpo thereby cleverly (not nefariously) leveraging the authority of the Shikage Menkyo awarded him by Takeda sensei (Takeda did Jikishinkage Ryu among other things) while avoiding any awkwardness that using the famous Shinkage name might cause.
Well, the Sho-Chiku-Bai forms come from the Omote-no-Tachi of Yagyu Shinkage Ryu, which Gejo Kosaburo trained in. Sho-Chiku-Bai is not a motif found there. I've seen the original densho of the founder, Kamiizumi Ise-no-Kami, the three major kuden-sho by Yagyu Munetoshi and his grandson, as well as some minor ones written by other headmasters and shihan, and it's not in any of them. I suppose there's an outside chance that there might be an obscure reference to it in some of the Edo Yagyu densho -- I haven't had the opportunity to sit down and read them start to finish --, but it's not in Munenori's Heiho Kadensho, and just about every motif in the other Edo Yagyu writings are found in there. In the Owari Yagyu line, the one studied by Gejo Kosaburo (the man Mr. Amdur surmises was the source for Ueshiba's Shinkage Ryu knowledge), it is not a part of the training. There are a number of phrases and concepts that pop up again and again, but I haven't seen or heard "Sho-Chiku-Bai" even once.
Perhaps there is some reference that he picked up from Takeda, who trained in Jikishinkage Ryu. I'm more inclined to assume he took it from its ubiquitous use in Japanese culture, and I'm not sure why you doubt it.