Okay, you win..it's not sankyo.
Throwing that out the window...along with the philosophical stuff about what "should or should not" be happening, and lets focus on what "IS" actually happening.
Roy has affected the center of uke and is controlling it already. He did this pretty much with kotegaeshi and then took uke down and pinned him. Then showed several options in order to further control uke with kimura, sankajo, sankyo...or what ever else you want to call a "bent arm" technique.
It was about the control first and the pain second. Again, it was a demonstration of various options you might have from that position.
The ability or inability to cause pain is always an interesting subject to me.
Why does ikkyo work? (actually mine doesn't so well these days!)
I think ikkyo works only because uke is moving to avoid pain, or the potential of pain. This is why it does not work so well on beginners I am finding today. They don't understand the dynamic of ikkyo so they can learn soon to counteract it! However, through in atemi (pain), then it works.
Nikkyo. Nikkyo only really works, I think, if uke is moving appropriately to avoid pain.
Sankyo. If uke does not back out around his center as you drive through it, well then he gets pain.
Yonkyo. Suprisingly I don't really like the whole radial nerve pressure point thing, but concur that it is best to drive the arm back into uke's center. But what keeps uke in position for you to affect his center? Avoidance of pain.
Same with the rest.
You cannot remove the potential for pain. However, as you state, simple reliance on it is not enough. I agree. Primarily the principle is about controlling center.
This, I believe, was a given in the video. That is center was already controlled.
If you lack that particular depth of definition in your technique, whether on the aikido or bjj side, you're not going to be taken seriously by either side.
Depth in definition? Well I tend to let the actions of what I do speak for depth. Either it works or it doesn't work. How serious I am taken is how effective I am at doing whatever it is that I do.
Anyway, pain or the potential to cause it is a motivator.
Okay, now someone will bring up the whole "Guy on PCP argument", and that you need to affect center and not use pain as it will not work.
I would agree! I would also submit that ikkyo, nikkyo, sankyo and the rest of what we train for, in principle, will be ignored and you will stand there (or not!) in great suprised at how ineffective you suddenly are!
So, what do we have left. Trying to control center, off balancing etc...all the stuff that we purport to practice in aikido. So while the techniques won't work, the principles behind them will...if you have trained them in the right environment, under the right conditions for a non-compliant uke that refuses to recognize proper ukemi and position to avoid said pain!
That however, begets the whole argument, if I filmed it and put it on YouTube...well, That does not look like Aikido!
So, when your ikkyo is ignored...what do you do? You clinch.
Then you move behind uke and take him down, (iriminage).
then you hold him down there in the ground in some fashion, or you immobilize him in some way so you can move on to whatever else you need to move on to. that might involve handcuffs, pain, or a blood choke. All options depending on the situation.
There is no miraculous bridge between aikido and BJJ.
The only reason we anyone is even remotely interested in the comparison between the two methodologies, is that they approach the same endstate resolution in a different perspectives in methodology.
So, it is important to those that have students in both arts, or to those of us that are trying to develop a breadth of perspective that might shed some light on things that we have not thought of before.
What is suprising to those of us that have and do study both arts, is that we can find similarities in the principles between the two arts. It may not look the same, but principally it is the same.
I was elated the day I figured out that the clinch involves the principle of ikkyo. Guess what, my clinch improved once I started looking at it that way. Same with my ikkyo!
So, it may not look like sankyo, it may not be the way you learned it, or that you may apply it, however, it does not mean that what is being done is NOT principally the same.
I do agree though that if you rely on pain then you are doomed for failure. It is a lesson that is driven home constantly in BJJ. If you do not control your uke in BJJ, you simply are not going to do anything with him. Painful or not.