He shoots a 600/4. That lens and the 400/2.8 are unique in that the lens collar and foot are well forward of the center of the lens, with the foot pointing rearward. He recommends placing the left hand on top of the tripod collar. The other long lenses all have a lens foot collar further back, with the lens foot facing forward.
Because of that, there is little or no room on a 600/4 to put your hand forward of the lens collar (look at some long lens images to visualize this).
It is my belief that, where possible, it is better to put the left hand on the far end of the lens, between the hood and the focusing ring (but keeping the hand off the focusing ring!), or on the hood/lens "joint".
It then takes far less pressure to accomplish more stabilization (far more efficient per unit of force). Then you can literally just let the lens or hood support the hand and let gravity do all the work. Pushing would then not add any value at all and would just exacerbate the nerve thing that Chris mentioned (interesting explanation, Chris!).
It is probably not possible to do it my way with Moose's lens (or maybe a 400/2.8) and you can visualize that in his image. His arm isn't long enough to reach .
I use my method with a 500/4, a 300/2.8, and some smaller lenses such as the 70-200 and 300/4. If I ever win the lottery and buy a 600/4 I may have to modify my technique!
(For years I thought Moose was "wrong" until it occurred to me that the different physical lens configurations dictate how best to do this)