I also have issues with wearing armor. I prefer the Dog Brother's style approach. You respect the stick that way. Shawn and I became fast friends and training partners when I first came to Ohio. We did this by using no armor and light bamboo sticks. Our bout lasted 35 seconds.
I really cannot comment as to why you cannot see how intricate that kote gaeshi was. Perhaps is was just the camera angle... But for the opponent to debrief with me that he believes he tripped speaks volumes. I was very proud of Shawn's growth in Yanagi principles of martial technique.
It's the throw at 3:40, and you mean kote gaeshi in the aikido sense of a wrist/forearm lock/throw? It's probably the angle/armour/video quality but it looks like the upper body was pushed over the weighted leg until his balance went, like sumi otoshi or similar I guess. When you're really nailed with that sorta throw it can feel like your leg was whipped out from under you. It could be very well be far more sophisticated and intricate than that.