OK, I think I figured that out, Brian...thanks for the pointers.
Here's how that bore cut works to increase the flex in the hinge. Look where I painted in a red line right under the apex of the horizontal and slanted face cuts...visualize boreing in right there, right in line with the front side of the hinge wood, right up to that intersection, but not past it. Let's first imagine that you bore all the way through the tree and exit on the far side in exactly the same orientation to the hinge. What you would have accomplished would be to make some room with that bore, as wide as the kerf, that would allow the hinge above it to flex further forward as the tree commits to the face before stresses begin to break it.
In green wood of a species that hinges well, this doesn't really help much, but in dead wood or species that are brittle, this additional room to flex allows the hinge to hold a bit longer than it otherwise would.
Now back up to the boreing again...if you only bore in partway, say 1/3 of the diameter, you have set things up to have the hingewood on the bored side to flex better and thus hold longer than the un-bored section. So the tree should swing to the side you bored.
In reality, I mis-stated when I said Richard "swung" that tree 40 degrees...what he actually did was faced it 40 degrees to the side of the head lean and improved the holding capability of the hinge on the opposite side with the borecut. It swung a little, but mostly he kept the hinge functioning even though the heavy lean wanted to rip it off early on the side against the lean.
When I asked him about the bore, he didn't go into an explaination of how it worked, he just said something like "makes the hinge hold better on that side". He also said, "if you take a block out right there, it'll hold even more". It took me about half an hour of chewing it over in my mind to figure out WHY it worked...but I'm pretty sure I have it right.