No doubt that jujutsu techniques found their way into karate as stated in my previous 2 posts on this thread. But to say karate is a subset of jujutsu is taking it way too far IMO. It seems you (or the book) are saying that if you take all that is not kicking or striking out of jujutsu you have karate, or what evolved into karate. In the Chinese "Bubishi" there are descriptions of White Crane and Monk Fist kung fu techniques that closely resemble modern Okinawan karate moves which were partly founded on these kung fu styles. There are also grappling and locking moves described in that book. I don't know of any Samurai teaching jujutsu to the Chinese? The Ryukyu Kingdom also had its native self defense "styles" that were incorporated into karate. Suffice it to say that karate is a product of several independent art sources blended together which came into its own by the early 1800's and further evolved throughout that century.