So what does the AIR and the DTR(Takumakai) have in common? I think you will need to explain yourself a bit more than just posting links...I'm still not sure why you think so. :0)
Chris, if I read Sagawa's "Tomei na Chikara", if I'm not mistaken, there's a part that says Takeda Sokaku Dai-sensei learned martial arts from Saigo Tanomo. Some people said Saigo's the adviser, but hey, that time, "advisor" is really your tutor, right?
Also the story that says AIR is a fellow koryu from Aizu area, where Takeda Dai-sensei came from, by using common sense, isn't that obvious that Takeda Sokaku Dai-sensei also learnt that skill, especially since he's from a samurai family.
BTW, I also heard the story from a thred in e-budo.com: http://www.e-budo.com/forum/showthread.php?t=9668
It's just oral history + common sense, my friend