When I joined the Ki Society back in 1976 with the Marianas Aiki Kwai in Guam (which was a sub group of the Hawaii Aiki Kwai) the official reason given for the split was that Honbu did not teach ki and would not allow Tohei to teach it as well. Looking at it all today, it appears that that was mostly just the front cover story. If you look at the books by Kisshomaru before the split, you will see that they talk about ki as much as Tohei did.
IMO, the real underlying reason for the split was simply ego, politics, and other unsavory stuff that boils up out of organizations from time to time and that there was fault on both sides.
I HAVE Yamada's book which contains an introduction from Tohei gives him praise as his "Master Instructor" and all of the techniques are "Tohei-Waza."