I think each sub group within Aikido has a certain look or feel that marks it, ASU included, and I wouldn't say that flexibility or variation was a mark necessarily for any of them, each of them displays that, and it is not, in my mind, the hallmark of ASU. The person who mentioned 'atemi' was not too far off the mark, in my opinion.
I think it comes from years and years of training and progression in that group, that to stay for any extended period you will be confortable with a central theme or feel put out by your sensei. There is one shihan I admire who displays a genuine desire to teach, and his students reflect that in their teaching of their own students. Another seemed to embody respect for the tradition of Aikido and love for the founder; I see that very distinctly in his students. One teacher I had had himself trained both in Yoshinkan and then under a particularly demanding Aikikai shihan in CA before starting his own style...another dojo's teachers told me they always know when they get one of his students, by the excellent ukemi (yeah, I laughed, our survival tactics)
I think, both consiously and subconsciously our teachers influence us, and we gravitate to that which is comfortable. So even if, through personality or size, we don't look like our teachers on first glance, there will be a basic thread in us that resembles the basic thread in our teacher. I can see that in ASU as easily as in Iwama or Yoshinkai or Ki Society, and it has nothing to do with how many variations of technique, or even the flow from one to another, since I've seen that in all of them. It seems to me to be something a lot deeper.