George S. Ledyard
I think this may be style specific. There might be certain teachers whose sword work doesn't have traditional parries but certainly the sword work I was taught had pretty much all the elements one would find in more traditional sword.
Saito Sensei's break down of O-Sensei's sword forms the back bone of what many folks consider Aikiken. But so many great Aikido teachers didn't follow that model that it's really hard to call anything Aikiken and have it mean anything specific. Gleason Sensei's sword work looks nothing like Saito Sensei's and Saotome Sensei's doesn't look like either one.
In my book what makes sword work "aikiken" is that the weapons technique is utilizing the same principles as the empty hand. One should be able to do a weapons technique and talk about how that applies in empty hand and visa versa. This was, in fact, what Graham was doing and I agree that it is useful for having folks understand their empty hand. The whole logic of Aikido (and Daito Ryu for that matter) is really weapons related since the samurai were really walking weapons systems.
However, given the wide range of what people even consider "aiki" in the first place, I don't see that folks will reach any agreement about what constitutes "aiki"-sword in any very specific sense.
My school's weapon work has lineage from Chiba Sensei/DiAnne Sensei (through one instructor) and Sugano Sensei (through another instructor). All I know is what some people traditionally call parries, our instructors have been very clear to point out that what we are performing is not a true parry. They use the term watershed in place of parry, there is some technical difference in which is beyond my grade to differentiate.