Okay, here I've gotta say "I don' know bout dat!"
I have the blessing(?) of being able to travel a fair amount in my job, and like to visit different dojo in my travels. One that I visit a couple of times a year is a AAA dojo (
http://www.seibukan-aiki.com/) in North Carolina. I was just there this week.
When Tajiri sensei taught what looked to me like our "koteoroshi", he still calls it "kotegaeshi". And from all I can see, it looks like he is actually twisting uke's wrist! His uke always flips over into a very satisfactory and noisy breakfall.
Of course, even there, I always perform the wrist technique the way Rubbert sensei taught me

and my uke's still go down, maybe not as noisily, but they go down. And Tajiri sensei never corrects me on that (on lots of other things but not that).
He demonstrated kotegaeshi in two ways from a katatedori attack. The first one was a tenkan that was exactly as I described it above. And the second one seemed much simpler; step to the side, hold your hand (the one attached to uke) in front of your face like holding a mirror, and using your other hand from underneath, peel uke's hand off (fingers to the non-thumb side). Then, still holding on to uke's hand, flip your now-free hand over to fold uke's fingers in and bring her/his hand straight down (kotegaeshi). This is an extreme twist to uke's wrist/arm and Tajiri sensei gave a big caution about the danger of going too far.
When we practiced that one, I made sure I picked out the smallest, gentlest person there, and we both practiced it very carefully!!!

Randy C