Thanks for explaining. I still don't get it, think you are using an unconventional definition of vignetting.
I'm not sure what the issue is. Perhaps it is that I said the on-axis "beam" is vignetted ? The beam is different from the on-axis ray. The on-axis ray is a single ray of light, but the beam refers to the entire cone of light from a point on the subject to a point on the image. (This beam vs. ray is standard optics terminology.) Vignetting refers to partial obstruction of the light path, typically at the edges. Here's another drawing:
Here I drew the full light beam from the bottom of the green tree to its image, on-axis: the chief ray is the black line, and the beam is the two blue lines (encompassing the rays in between). The off-axis beam from the top of the tree is the magenta lines.
If we interpose a too much under-sized aperture behind or in front of the lens (the vertical black lines), the on-axis chief ray goes straight through, but the aperture will partially obstruct the outskirts of the on-axis beam (the blue lines). This is vignetting the beam. It will form an image of the bottom of the tree, but slightly dimmed. It will vignette the off-axis beam more, of course, so the top of the tree will suffer more light loss.
I am not an optical designer, but I talk to optics people frequently (I'm an astronomer) and this usage of "vignette" is common.
As the diagram suggests, the size of the obstructing aperture or baffle (like a rear shutter) that you may be able to get away with really depends on the angle of view and the geometry of the situation, there's not a simple rule of thumb for it.