I liked her article. I agree that connection is difficult to define and teach. My wife and I have had many spirited conversations on that!
Two things that stood out for me, and they have been a long standing debate for myself.
I sometimes see myself as half of the equation, and I need to "fit" with the forces at play. Tenchinage is a common example for me - I want uke's shoulders to go heaven and earth-ward, and sometimes not so much my own. Uke and I are very much joined. Saotome sensei in particular was talking about this.
The fourth teacher was talking about finding his structure and intent. I had one teacher talk about, "make the shape and go," and Tohei sensei's writings seem to talk this way too as I recall. With my own structure and intent under control, I can just move. I don't need to pay much attention to uke or how I contact uke. I just move, and they connect however they will. I sometimes do this in randori.
There are many different ways to teach these things. I did not expect the variety of teaching methods and language within one association.
Are they all talking about the same thing though? I think that this goes to the core of aikido as an art and why i think it's basically a post modern art. There are no set parameters or definitions for anything: there are a set of terms that act as floating signifiers: concepts that you ascribe your own meaning and value. It's what has allowed aikido to become popular but also is its Achilles heel.