MJER is kinda hard to talk about in general terms. There is one large branch and several smaller branches. The book you mention was written by a member of one of the smaller branches. Why multiple branches? Politics. Egos. Who knows. Doesn't really matter.
The Seitokai branch, which is the larger branch led by Ikeda-soke is a bit different especially in the ranking area. To my knowledge there are no hard and fast rules on "time in grade" such as there are in some other branches. There are some general guidelines, but everything is pretty much at soke's discretion. There are also no kyu ranks. The only branch I know of that uses kyu ranks is the Jikishinkai led by Miura-sensei.
The history in the book you have is pretty much true for Seitokai right up to the point in the lineage chart where you find Oe-Masamichi. I believe that's where the author's branch split from the seitokai line. Of course, I'm not a history buff, so I could be off on the accuracy of the information in the history sections.
If you are interested in checking them out, there is a Jikishinkai dojo in Chicago.