One theory that I've heard suggested before revolves around the fact that Okuyama-- the third-generation headmaster of Jikishinkage Ryu-- was apparently one of Kamiizumi's earliest students. At the time that Okuyama studied under Kamiizumi, Kamiizumi might have been in a "Kashima phase," not yet having switched his emphasis back to Kage Ryu. Another possibility is that Okuyama himself came from a Kashima-oriented background and viewed his Shinkage Ryu training through a sort of Kashima lens. As you say, it ends up being something of a split source, with some Jikishinkage stuff being readily identifiable as Shinkage while other things seem to hail from Kashima (my opinion, of course-- those more knowledgeable may well disagree).
Originally Posted by Nathan Scott
I personally think that a good way to think about Kamiizumi is to compare him to Ueshiba in modern times. You have a martial artist who lived for a long time, was exposed to a lot of different stuff over the course of his career, and taught students of all different backgrounds according to their abilities. So a student of Ueshiba's might get something different based on when he studied with Ueshiba (the whole pre-war/post-war dynamic, etc.) or because he came to Ueshiba with a very different set of skills. After he got Ueshiba's teachings, he might take it in very different directions based on his own past-- think Tomiki and Mochizuki. Given that Kamiizumi had trained in most of the major sword lineages of his day-- Kage, Kashima, Katori, Nen, etc., and trained veteran swordsmen who had originally trained in a diverse collection of schools, it would be strange if the lines descended from Kamiizumi didn't reflect a rich diversity of influences.
"Cuius testiculos habes, habeas cardia et cerebellum." - Terry Pratchet
My opinion is, in all likelihood, worth exactly what you are paying for it.