So this system is much the same as Kirby's system. Jay studied Danzan Ryu under Okazaki. It was Okazaki that studied the more classical systems of jujitsu. Okazaki studied 3 of them, and then added Lua, Kung fu, Boxing, Wrestling and the rest. Jay studied under Okazaki, learning "classical jujitsu" but the "classical jujitsu" was already a "classical hybrid jujitsu." Yes, Jay then went on to add more Judo and then his own take, making Small Circle a hybrid system as well. Thus, Budoshin, Danzan Ryu and Small Circle (and a host of other arts) are all modern hybrid arts. They are all good arts, and the effectiveness of each will be based on the method of training used.
Questions of lineage are (at their best) factual questions, though the facts can get blurry from time or obfuscation. Questions of purity are often emotional, value-laden judgements. At their best, I think purity questions are about historical accuracy. At their worst, purity questions tend to be about “protecting” an art from evolution, accommodation to cultural and legal changes, and questions about the purposes actually served by the art.
Calling Japanese Ju-Jitsu a “hybrid” of these gets the order wrong, and thus is misleading about the scope of the arts. Perhaps my biology training is making me pedantic, but the parent isn’t a hybrid of the offspring. It would be more accurate (if, perhaps, provocative) to describe the descendants as (evolved, highly focused) subsets of the the parent art. If you’re simply trying to explain Japanese Ju-Jitsu to someone who is familiar with judo, aikido, and karate then it could be helpful to say that Ju-Jitsu includes the techniques found in each of these
I would like to say budoshin may or may not have a murky past depending on you view to it's historical lineage but the guy got instructor of the year in by black belt magazine 2007 it's a lot like a mix of judo and aikido but they do strikes it's very solid art imho and Id say bjj is my first art but I've ranked judo and old skoool Japanese Aikido