I think stiffness definately has something to do with it. One of my old instructors intervened between this drunk bloke who was beating up his wife in the street. The drunk bloke turned round to punch him and he did kote-gaeshi. He said he was amazed how well the bloke flipped over. Also, when I was just starting I was thrown with kote gaeshi by Yamada and he definately was able to flip my body over without me having to go over in any way - he had complete control over where my body was going. I landed perfectly.
I think a lot depends on how you do the kote-gaeshi. Yamada sensei has some great circular movement in the vertical direction. Some peopl emphasise the movement of the arm over the application on the wrist.