From an interview
with Saito Morihiro
To the best of my recollection, Nishio Sensei usually executed "koshinage" that were adaptations of judo (much like ogoshi). Kuroiwa Sensei created a unique technique that was actually an adaptation of a wrestling single leg.
John Driscoll has made an almost impeccable case
that koshinage, in the "classic" aikido manner, where nage's hips are perpendicular to uke's (rather than judo's parallel) is the single, solitary aikido technique that is not derived from Daito-ryu; rather, from Yagyu Shingan-ryu. This article is kind of buried on the Aikiweb site - it deserves to be highlighted, for it's meticulous consideration of a single technique (John is a high ranking judoka as well as aikidoka, by the way). It also is a prime illustration of how a study of history can actually illuminate proper practice.
A claim that I heard once from Saito was that koshi-nage was originally practiced with the nage standing upright - koshi garuma rather than what we think of as koshi nage today. The change (supposedly) was made because the ukemi for koshi garuma was too difficult for most people.
Muddying the water...Anyway, it does make the perpendicular hips seem logical, if you think of it in that context.