For the record, I believe kashi refers to legs.
That would be "ashi." "Kashi" can refer either to "oak" or "confectionary." Unless there's some kind of set of techniques involving the two...
As far as that particular kotegaeshi counter goes of uke launching nage while uke is still in the air, I think it's more for show. We've practiced the counter for kotegaeshi wherein you take the backfall or breakfall while continuing to extend nage's motion of the kotegaeshi to break their balance to throw them. The same can be done for shihonage and (although I haven't tried this one out yet) kaitennage.
I don't know if it's a technique I'm going to be trying "on the street," but I think it helps illustrate the fact that falling and rolling doesn't necessarily mean that uke is no longer a threat and that breaking nage's balance can happen in the most interesting places...