Here's my opinion, Having been a Photographer for over 40 years I do understand the triangle But everyone raved about the book so I bought it. I thought it was a pamphlet and a vehicle for him to show pictures of his hit wife and brag about it. But everyone loves the book so what do I know.
Here's the thing with your DIF question, When framed equally, ( Equal magnification) Distance to subject and focal length cancel each other out and you will have the same DOF no matter the Focal Length/Distance to subject. So the only thing that will affect DOF is Aperture.
As far as him recommending f/22. Yes it will yield the greatest DOF but it will also introduce Diffraction within the lens and cause the image to be soft, especially on a cropped sensor camera.
As far as Hyperfocal distance goes, it's not the cure all to everything. It provides for the maximum DOF for a given Aperture. However it doesn't provide for the sharpest image, especially if you have a singular subject close to the camera. The sharpest point will be the point of focus and everything else is just wintin the field of acceptable focus.
The best of all worlds were to place your subject at the point of focus and that point being the hyperfocal distance also. So your subject would be the sharpest and then you would have a filed of focus from 1/2 the distance to your subject to infinity.
The reason that a wide angle lens will appear to have a deeeper DOF, has to do with perspective compression of bringing the background into closer view with a telephoto lens. You can then see that the backgrund is OOF even though the DOF is exactly the same it just to the eye doesn't appear that way.
You also have to take FOV into account with your Gecko shot. The shot's BG will look entirely different shot with a 18mm at 1' DTS than with a 180mm 10' DTS
The reason he suggests metering the blue sky is that in essence you are turning your Camare's Reflective meter into a Incident meter and metering the light that lights the scene (skylight) instead of what is reflected off your subject