vidrazor statement 1: "I'm not buying that rap about off-axis falloff. If his explanation were true, edge centers would be just as dark as edge corners."
I assume you are referring to this image
Still wrong, but maybe this will help you understand. I added a blue oval to my simple example. This should represent the off axis vignetting on both the left and the right (looks close to a catseye doesn't it?). Again if you notice more is clipped from the corners, not the edge centers as you believe would be the case. And this line is not a hard line, instead it is a gradual loss of light from the center of the image circle to the ends, but since the edges of the sensor are CLOSER to the edge of the image circle, they are darker.
vidrazor statement 2: "The only reasons I see for falloff are that light travels further to reach the corner, and also strikes element surfaces at sharper angles, losing additional light."
Do you have any evidence to support this statement? Seems like you are taking a guess, but not really understanding why. I believe you are confusing this with Spherical Aberrations mixed in with the separation of light, or Chromatic Aberrations. Stand in front of a mirror. Now stand to the far left. Now the far right. Is there a lot of light falloff? The sharp edges don't matter . . .
REF 3: http://toothwalker.org/optics/spherical.html
REF 4: http://toothwalker.org/optics/chromatic.html
vidrazor statement 3: "Stopping down collects only light rays traveling in a more parallel direction, evening out illumination"
Wrong again. A 50mm lens on an FX sensor has a field of view of 46°. It will collect light within this field of view. Now imagine a cone of light starting from the aperture blades at 46°. If you are shooting wide open, then your cone is much larger (still 46°), but it is too large to clear the lens barrel. Now imagine stopping it down to f/22, where the opening is much smaller. Therefore you have a much smaller cone of light, which is able to clear the lens barrel. Now there should be a certain aperture where the amount of light is small enough to completely clear the lens barrel. This is the maximum aperture you can use where there is no vignetting from light fall off.
You can visualize this in the following image. The red bars indicate the exit pupil (aperture). In this image, the lens at an f/11, and no light falloff for this field of view occurs. If you were to open the aperture up more, your cone would be fatter (same angles) and be clipped by the barrel. It is called natural vignetting, and has nothing to do with parallel light (does this even exist?)
Believe what you want . . .