I only know what you have told me. You have told me that anything done with aiki can be properly called aikido. If I accept that statement as true, it logically follows (since aiki is not exclusive to our particular martial art), that many different martial arts and activities could be accurately and properly called aikido, at least some of the time. And if that is the case, then the term aikido cannot function as the name for our particular martial art.
Mary is the "apple" of my eye, I have an Adam's "apple", I work on "Apple" computers. Do any of these uses of the word apple prevent it from functioning as the name of the fruit? Aikido is a Way, a process of discovery. A Way that is delineated by a set of principles that have come down to us through O Sensei via his own process of discovery.
The word Aikido in that broader sense can be associated with almost any activity if the activity is performed in accordance with Aikido principles. While we wouldn't call basket weaving done with mind/body coordination Aikido, mainly due to the conventional notion that Aikido is a martial art, we would not be unjustified in doing so. Many words do not have precise, mathematical-like definitions. In fact, many words are their own opposites. When it comes to word usage you have to consider the contextual framework that the word is used in.
Perhaps as you continue your training you will come to see Aikido in a richer context that allows for a broader definition of the word while not preventing it from functioning as the name of the art we practice.