My guess (and it is only a guess; I don't own a 5D2) is that it is a combination of two or three issues:
1) Tolerances. It happens with some cameras, not with others. Canon lenses are tested so that they work within the tolerance.
2) Someone commented that it only happens at large apertures. For smaller apertures, only the middle of the lens is used, and then it doesn't happen, so this means the problem has something to do with the edge of the frame, at the shutter or closer to the lens. I guess this was already known, but if you combine this with unchipped lenses, the camera doesn't know how fast (largest aperture) the lens is. This brings me to the point: I think that the 5D2 might have a variable shutter speed, and uses only the fastest speed when the camera thinks it needs it, i.e. fast lenses wide open or somewhere near, at high shutter speeds. In other circumstances, it uses a slightly slower shutter speed, possibly to prolong shutter life, or... to make it quiet:
3) Silent Mode slows down the shutter (even more?), when it can. It might be that the variable speed shutter is only effective when Silent Mode is active... Can someone test if Silent Mode is actually more silent at 1/8000s with a fast chipped/EF lens wide open? My tip is that under these circumstances, it isn't actually more silent, because under these circumstances, the shutter must run at full speed to avoid obscuring part of the image.
I don't quite have the overview on all the facts here. Samuli, does this fit all your facts? Live View must somehow exacerbate the problem, but I don't yet see why. I guess it just changes the timing, since the shutter can be fired without first waiting for the mirror to go up.