I think most of your

I think most of your analysis is dead on on this one, although I'm willing to give the practitioners in the video benefit of the doubt to a certain degree. The look like they might be performing their demonstration in fairly restricted space. Kote-gashi can frequently be a technique that uses up a good deal of mat space when the attacker is properly lead after the initial attack...maybe they felt they didn't have the space to safely do it and the instructor simply tried to shorten his lead. As for the pinning technique, what was demonstrated wasn't what I was taught either, but I have used a finish almost the same as what was shown as well. The biggest diffence is that I would actually step further up past the head and keep the arm totally straight. At that point, keeping kote-gaeshi is unnecessary, I can simply cup the wrist in an open hand and drive my body weight down into his shoulder and neck. Again, not what I was originally taught, but a viable finish..especially if you become aware of other attackers coming from the direction of the prone uke's feet. The uke's is now blocking their most direct line of attack.