Agree 100% !
There is no right way based on turning the wrist this way or that, and many of us think the wrist is sort of besides the point...
Um, I'm not so sure...If I go completely from my own personal experience, I would have to disagree. I have had forms of kotegaeshi applied to me that were completely ineffective and other forms that were just the opposite. I have never had an effective kotegaeshi done to me without a wrist twist. I have had people try to substitute a cut of the arm at the elbow or a strong pull from my dogi sleeve for the wrist twist but on these occasions the result was not anywhere near as effective as kotegaeshi done with a wrist twist. I find also that forms of kotegaeshi that stretch out my arm rather than bending it at least somewhat back on itself are extremely vulnerable to kaeshi waza.