Personally, i disagree with any claim that there are more than one aikido traditions. There is only one aikido, although different aikidoka, have different personal styles in the way they execute the techniques. For example, in an other thread i had a conversation about how different is the current Doshu's personal style than Sensei Steven Seagal's. These personal styles however, do not constitute different aikido traditions. So in my opinion what Mr. Tohei, Mr. Shioda and others did, claiming their own styles is wrong, regardless of their effectiveness.
It isn't really about how individual practitioners execute techniques. It is about how the training differs, how the art is transmitted. I am not sure if you intend for your post to be as hyperbolic as it sounds but the fact that ki society, yoshinkan. iwama, and mainline Aikido have differences in training methodology is patently obvious. That's what is meant by "different style."