Tony,
The green's construction method would be best described as push up...I guess. Except nothing is really pushed up, shaped in place is more like it.
The soil there looks to be quite fertile and tests out very well, especially the chemical tests as the pH is right where you'd want it and nutrients and minerals are in a nice balance. But, its taken thousands of years to get that way and all you have to do is drive around and see other scars such as utility trenches, construction disruption, and other areas of disturbance to see how long it takes for the soil to heal. Its a fragile environment and best not to disturb unless necessary. We'd like to hand over a course to Jagger that can be maintained with a low input emphasis rather then constant remedial work which is more common in golf construction.
As far as using the cultivator instead of the rake, the cultivator pulls up organic material that then requires more hand raking to collect and remove. Hand raking is slower, and more labor intensive, but a better approach if all you trying to do is get a clean seedbed with a minimum of soil disturbance. Also doesn't hurt that a rubber tire machine, even one with as light a footprint as a sand rake, isn't spinning endless donuts on your top soil.