I have thought it over and I think VR can not have such an effect on bokeh. In theory (geometrical) there is a perspective shift due to camera shake (you do not shake with the entrance pupil location as the center of the shake). But the shift of background plane (defocused area) during exposure is neglibly small, too small at all to cause such an effect.
The graphics on http://bokehtests.com/Site/Stabilization_and_Bokeh.html are extremly exaggerated in scale. Keep in mind the sample picture of the deer : 600mm lens; shooting distance was maybe 70 meter (+ background additional 10 metres).
Furhtermore if VR has this shift effect to the defocused areas the effect would cause some kind of motion blur and not "double lines". The effect that was shown here in sample pictures occured with super tele lenses and tele zooms. Most telezooms show some kind of over corrected spherical correction in the tele range and together with the high amount of defocusing effects (which the human eye does not notice in normal vision) the "bad bokeh" appears. So in the end Nikon answer was OK.
As the author of the exaggerated graphics that you referred to, I have to say, you are correct... I massively exaggerated the picture to illustrate the point, not to show EXACTLY what happens in the lens. Anybody who can't hold their lens steady to the point that it shifts 45 degrees each way is going to have some blurry pictures! BUt the point is still valid. Just as you wouldn't shake as much as that, you also would not have the image shifting from the left side of the picture all the way to the right. BUt the question is, what if there is a 1 degree shake, or a 0.1 degree shake. How much image shift would there be due to parallax? I intended to figure this out but then went on to bigger and better things, and have still not made it back there. ONe thing is sure-- the distance a pixel will travel due to parallax and a 0.1 degree shake will be much more on 600 mm lens than a 24mm lens.
As for your other point, I also agree. A unidirectional shake will produce a motion blur. But this will only occur if there is a single direction shake... if you shake from left to right ONLY during a photo. The minute the lens moves from one direction to the other, you will get a longer exposure for the object right at the point when directions change. and if you change multiple times, you will get two or more bright lines each time you change directions during your shake. So it is less important, or completely negligible, if your shutter speed is very fast. But if your shutter speed is slow enough to involve at least one change in direction you end up with a motion blur and bright spot. If you have time to change directions in your shake twice, you get the double line effect as I described on my website. Think of a very fast strobe light doing multiple exposures on a pendulum.... when changing directions at the edges of the trajectory the images will get closer and closer together. The faster and faster the strobe becomes, the closer you get to a real long exposure, and you will see images bunch up on each other at the edges. THis is the same as I am talking about, only the LENS is the pendulum.
The effect of VR is just that instead of having a big motion blur evenly throughout the image, the "in focus spot" is stabilized to a certain part of the picture. The effect described above will be more amplified the further away from the "in focus" spot is.
Now, as I have said many times, I am not a lens designer, a physicist, an optical engineer, or even a professional photographer. I am just an amateur photographer who finds this stuff very interesting, who has been burned by bad bokeh before and wants to understand it. So I may be wrong here. But I doubt it. Parallax is definitely a REAL phenomenon, and should affect ANY image with ANY lens that is rotating around any point other than the entry pupil, and should also be there with non-rotational movements as well. The reason it affects BOKEH in image stabilized lenses is that motion blur in the in focus area is stabilized. BUt again, it depends on how fast you shake, how long the lens focal length is, how long your shutter speed is, etc. And while I have very little doubt this phenomenon exists, the question is-- is it big enough to be relevant? Perhaps the shake when translated to the image only accounts for a motion of 0.0002mm at the sensor plane.... well, you won't be seeing this effect then.
If anyone can do the math that would be great. I can do it, but it will take time because I will have to figure out how to do it. If anyone knows and could tell me or do the calculation themselves, let me know!
Sorry for yet another very wordy reply.