That's my understanding as well. I find it hard to imagine any exercise that had been initially taught by OSensei would be considered by any other of his uchideshi as outside the realm of "Aikido training". Kurita Minouru (uchideshi to Osensei, who left with Tohei after his death, only to leave that and go independant) said/implied (so hard to tell when what's being translated for you is subtle Japanese) that the Ki exercises were from Tohei's own study and quest for understanding about how OSensei actually could do all the things he could. Now I'm not saying that OSensei didn't do these things, or consider them important, but I don't think he was the source for them WRT Tohei or the Ki Society groups. Much like today it seems that serious students were exploring other paths for understanding. I think that's frankly always been the case, regardless of the art.
Tohei did indeed start a lot of the Ki-exercises stuff while he was under the aegis of Hombu Dojo. The fact that O-Sensei didn't stop him or indicate that Tohei was adding something foreign to Aikido should be a telling point. So in terms of "transmission", Tohei was (at least to a reasonable degree) propagating a core aspect of Aikido, even though technically it would appear to be something peripheral, if someone is just focusing on the "transmission of Aikido by Ueshiba Morihei". So too narrow a focus on the exact ritual and exercises is not warranted, seemingly.
The Ki and Kokyu skills can be done at many levels of ability and sophistication and they can be trained in a number of different ways, as long as someone understands how the development and usage is done. So what happens is that there are essentially two things that need to be watched, in terms of "transmission": the historical development and teachings of Aikido in general; the transmission of the core skills of ki and kokyu.
Because of the different viable approaches to ki/kokyu skills, it's easy for someone not conversant in the skills to tend to see many of the Aikido offshoots (Yoshinkan, Ki-Society, etc.) as being side-branches of the main transmission. In fact, someone like Shioda, Tohei, Inaba, Sunadomari, or others, may be fully within the mainstream idea of the initial transmission, even though it appears that they are off the main development/transmission. It is the eye of the beholder that may be fooled, if the understanding of the ki/kokyu skills is not something he has. Note that I'm leaving open the idea/fact that many of the students of all the varying factions are ignorant of these skills; that doesn't mean the founder of their lineage was bereft of those skills, though.
So to point out the previously-styled steps of Misogi in terms of valid transmission is perhaps being unnecessarily focused in adhering to the proscribed rituals. The actual idea of transmission encompasses training like the Misogi steps, but the core ideas of Ueshiba's Aikido can be fulfilled in a number of other ways, as long as the training and practice result in "aiki", IMO.
Shioda's Aikido (for example in this video:
) may look somewhat different from what Ueshiba is doing, but the principles are exactly the same. Tohei's or Sunadomari's Aikido may look widely divergent from each others' or from Shioda's, but the basic principles are the same. Do they adhere to the steps of Misogi as outlined? I doubt it. But it doesn't really matter because the actual "transmission" of Aikido entails certain principles, not rituals.