Phillip,
good explanation.
I think in simpler terms, Tillie is saying that most greens are front to back to help hold/stop a shot but that you can create a preferred fw position simply by also sloping a green right to left of left to right, making it easier to hold from one side of the fw than the other by virtue of hitting into the upslope, rather than hitting into an effectively level, or slightly falling away slope to the far side.
I think if you look carefully, many greens by several designers are actually concave (raised a bit on both sides with a valley in the middle) as well as raised in back all to help hold any shot that hits the green on the green, which helps average golfers more than they know.
Making only one side concave does enhance strategy for the better player considerably, and they are probably the ones who would be most likely to notice that subtlety. However, its that kind of thing you need to incorporate if you want a great strategic course.
And, "purists" whatever that is, could argue that soley by tilting the green, you could create enough strategy to eliminate the need for fw or even green side bunkers, although they could easily complement the strategy, as could the axis of the green.
With the emphasis on designing for the better player, I think we see a return reverse slope greens, but the thinking is the margin of error is smaller and it will require a really high spin shot to hold the green or the golfer will need to play a bit short of the pin, perhaps bringing surround bunkers into play a bit more, because his ball will roll out a few yards, rather than stop dead or back up.