OK, as luck would have it, I am currently teaching fin kicks, including the back kick, to someone who is an expert on this topic. There are two topics in this thread. The first is the one Lynne raised, and the second one was implied (but not stated precisely) in my observation that the technique being described here is not the same as the one I originally learned from the same teacher. I assumed there must have been a reason for the change. I thought a good reason was that the old method (fin tips pointing down and out to make the front of the fin the primary source of resistance) tended to push water downward toward the silt, but I questioned its power since the sidewalls of the fin had less surface area to provide the resistance for propulsion. When I tried it, I was surprised at how well it work. I showed my student both methods, and he was able to talk about both issues from an expert point of view.
1. Lynne's Original question: He sees no reason why pushing the fin tips back at an angle would be any different from going straight back. He is with Lynne on this--it shouldn't matter.
2. Relative power behind the two techniques: He wrote out the equation for calculating drag force, but I lack the ability to make the symbols here. The key concept in the equation is that the most important factor is the velocity of the movement. All other factors in the equation are multipliers, but velocity is a multiplier after it is squared. In examining the shape of the kick, he observed that, yes, the older (to me) kick style provided more surface area to create drag, but, perhaps, it is more awkward and less efficient because of the anatomy of our legs. The method being shown here allows more velocity, and because velocity is squared, it makes up for the lesser surface area. If you are able to perform the motion twice as fast, you get four times the power.
We also talked about my opinion that it is important that the recovery stroke be done slowly to keep from cancelling out the effects of the power stroke, and he said the same principle applies. If your motion is half as fast, the power is 1/4 of what it would have been.
He edited this post before I sent it. I hope it is helpful.