I am enjoying many of the comments, it seems the discussion has gone in several different directions from its origin.
Did anyone teacher teach "aiki" to anyone else. That really is an impossible question to answer. The first problem is in the definition, depending on a definition it is yes, or no. The man that started all this aiki thing is Takeda. He is the gold standard. Problem is, we have no idea of how good Takeda was. The only recorded information we have access to publicly is really his students account. I would consider others, like the ones he killed using aiki can't say a thing, as they are dead.
Ever since Takeda died people have really no idea of his skill. Creating the question of how it compares to his students aiki, who had Takeda's aiki. Was it the Founder who defined Takeda's aiki or not.
There is a world of speculation based on Takeda's student's accounts. I have been exposed to many definitions of what aiki is or isn't, as we all have; people's opinion on or off the mat. Who really knows Takeda's aiki. His students did, like the Founder and the other thousands of people he taught. Yet, no one comes up with a discernible standard definition everyone agrees upon. The Founder included, I believe had no interest in doing so because that would place all the credibility in one man's hands.
Sadly to say some have taken the ambiguity of aiki and exploited it selfishly instead of objectively and altruistically for the purpose of the truth. They really muddy the water even more.
When there isn't allot known about a well known person's life and personality, people fill in the gaps with speculation and assumption. It is human nature to try and complete the puzzle. Very little known about Takeda's personal teaching style making it ripe for speculation. What is known of Takeda's aiki points with in the context of the times, how he thought of himself and the life-style he lived. They did call him the "Last Samurai." Many of the Founder's deshi feared him, and disliked him. He was demonized in Aikido because of that for generations. Again furthering the mudding of the water of the definition of aiki.
The next logical step then to find a definition of aiki is to look at Takeda's students ability. There are said to be somewhere around 30,000 students of Takeda's. Now who got Takeda's knowledge and who rose to the top, and who got both is the question. Traditionally, it would be his youngest son who would get "the goods." One of Takeda's students thinks differently, and there are where a couple of other students whose skill surpassed Takeda's son. Both of those students claimed their aiki surpassed Takeda's. Each student displayed a different skill unlike each others. Those comments need to be taken in context, as we don't know why the purpose for those comments where. Making assumptions would further muddy the water more. It would then be wise to see these comments showing that even Takeda's students had different definitions of aiki.
This leads us to the Founder, who had a role in Takeda finding the right lexical for his ability. Even with that we can't measure the Founder's aiki to that of Takeda's based on finding lable, which isn't a definition. What we can measure the Founder's aiki up against several other accomplished Takeda students to form a definition. The issue with that is there is no common experience agreed upon to define aiki. What results is individual definition competing to be the definition. An effect of compounded is the students of each student of Takeda's divide in to camps who enforce their instructor's aiki as being "it." We move farther and farther way then in defining Takeda's aiki and what aiki is.
I will not mention the input of others on the outside of the situation confusing the definition aiki with their definition and skill. It only distracts and further confuses the issue.
Awkwardly put, language helps us define aiki. But only in part in its limitation to describe an action in words to verbally communicate to others an experience. Ideally, it is the combination of language and experience for a common experience we can all agree upon as a definition. Will we never know what the gold aiki standard or definition is to be. Rather then ending there, a greater gap of knowledge is created, what did Takeda pass on or not pass on to his students including the Founder. The Founder was talented no doubt. Out of thousands of students he did raise to the top level. A level where he still sits alone. As Matt said and I do agree, it is all academic, because it really is about individual success. It has occurred to me, maybe this is why there is no standard lexical definition. The definition then is seen in Takeda, and the Founder who could put their skills to a measurable skill use and not at a theoretical use.
Thank you everyone. Have a good day.