The idea is this: you set the camera's exposure to set the diffuse highlight value of a subject; with digital positive medium and a caucasian-skin-toned person, this is pretty close to a direct, un-compensated, incident light reading. So, meter the subject using the incident light meter, and set that exposure on the camera.
NOW....using _____ANY_____ color of background paper, wall, or canvas, you can determine the density/color/value of the background by using a ____reflected____ light meter reading made from the camera position.
If you have a white piece of paper as the background in the studio, it takes very little light to ensure that it renders as white;
If you have a gray seamless paper, you'll need MORE reflected light making it back to the camera sensor to render as white;
If your seamless backdrop is BLACK velvet, it needs to have a LOT of light blasting at it, so that the light that comes back to the camera sensor drives the black up to render as white.
The system is based on setting the diffuse highlight by metering the main and fill lights, and any other lights that are on, using an incident meter reading, not a reflected reading and setting that exposure level on the camera....a black car and a white car will have hugely differing reflectance values, so that's not the way this system is set up.
The light that actually makes it back to the sensor or film...from the background, MUST be metered at camera distance; one could meter using the incident meter's hemispherical dome, measured at the background, but a white, a gray, and a black backdrop would ALL have the same "incident" value, but the reflected values would be wildly different.
This is the part you're missing out on understanding: incident meter's reading = the actual exposure set on the lens for the subject, in f/stop value. Reflected light meter's reading froim the CAMERA distance!!!!; this reading is used to determine how much more, or less, light is actually hitting the sensor or the film, using _ANY_ color of backdrop paper, and the difference in this reading from that of the exposure used on the lens, determines how bright or dark said background will be rendered. That's why he specifically mentions the reflected meter reading's differential from the diffuse highlight value, which is what he calls the exposure setting's f/stop.
The white and black values he mentions are the degree of difference (in f/stops) in a reflected light meter's reading when that reading is made from camera position,and he expressed white, and gray, and black background values, in f/stop difference from f/stop the lens is set to.
Using incident metering on the subject is the basic idea as to how to set the lens's f/stop for the main and fill light set-up in use. Then, to determine if the background is white,or gray, or black, regardless of the actual reflectance value of the paper or canvas or wall, then the "differential between the exposure, and the quantity of reflected light that hits the sensor" becomes the way one can predict the value/color/hue of the background that is rendered in the final picture.
There are actually two exposure values that must be considered: one Exposure Value for the subject..and an Exposure Value for the amount light that strikes the background and which actually travels allllll the way back to the camera. Keep in mind that the background and the subject might be 5,10,15,20 feet different from one another, PLUS there's the distance from the background paper and then the distance from there and back to the camera, and there's a range of background reflecting ability that tremendously affects the "brightness" of the backdrop in the final picture...this is why the background density MUST be measured, by a reflected meter, at the CAMERA position.