//Anne Marie: I appreciate your step-by-step instructions. They are clear. With that in mind, I took David's advice and looked for tsuki ikkyo ura videos and I found this:
The video is what I was trying to describe. The video I provided (which is the USAF 4th kyu test requirements), the nage did not properly lift the arm up across of him in the front, yet he also did not do a 45 degree rotational turn. Tenshin is not necessarily a big 45 degree rotational turn. It is step back on a slight diagonal. If you take a 45 degree step then you will to far away. In my video, he is demonstrating 3 variations to Tsuki Iriminage. The third and fourth ones are his best attempts with a tenshin opening. In the third one, he stepped straight back, and look what happened - he got hit.
In the video you provided, the nage is not stepping exactly straight back, either. Watch his legs and hips. He is stepping back slightly off the line of the attack and rotating his hips to continue to be off the line of attack and to draw uke off-balance. If you step exactly straight back you will get hit by uke's tsuki. Watch the foot movement and the hip rotation, nage is taking is off the line of the attack.
Also notice in the video regarding the "grab", he is not literally grabbing uke's punch in midair. He glances his hand down uke's forearm and lets his hand slide down to uke's wrist. You can not grab a punch. If uke had a knife, you could end up grabbing his blade.