It's actually quite simple: the effect of shake is dependent on field of view,. not focal length. It just so happens that focal length gave us a convenient way of doing the calculation, but if you change sensor size, you nee to throw out that calculation, or at least modify it so it really does end up produce the same answer for the same sensor size.
It is easy to demonstrate that the effects of shake are dependent on field of view, not focal length. Consider a P&S camera with a "150mm equivalent" lens (which might really be only 35mm in actual focal length), a DSLR with a 100mm lens that is basically 150mm equivalent in field of view, and a film camera with an actual 150mm lens. Same field of view on all three, but *vastly* different focal lengths.
Set all three cameras on a tripod and point them at some distant object. Since the field of view is the same, the should should the exact same scene in the viewfinder. Now, rotate all three of the tripods by the exact same amount - say, 1 degree of rotation. Is there any doubt in your mind that the object that used to be centered in the viewfinder will now be off-center by the *exact same amount* on all three cameras? Of course it will - because they are showing the same scene.
Now replace (or zoom) the lenses so they are all at 35mm equivalent. Again, they actual focal lengths will be *vastly* different (probably 8mm, 20mm, and 35mm respectively). Again, though, if you point them at the same distant subject, because they have the same field of view, they will show the exact same scene in the viewfinder. And rotating the tripods by 1 degree each will result in shifting the scene by exactly the same amount in all three cases - but of course, being a wider angle of view to start with, the shift won't be nearly as noticeable. Yet the full frame camera is at the exact same focal length the P&S camera was in the first example. That is to say, 35mm as a focal length on the P&S camera showed a *big* effect from the rotation; 35mm as a focal length on the film camera showed a much *smaller* effect - indeed, the same effect as the P&S showed at 8mm.
Consider camera shake to be the equivalent of rotating the tripod. What this shows is that the degree to which a given amount of shake affects the image is the same for the cameras with the same field of view. Change field of view, and you change the effect of shake. Focal length is *not* the determining factor - field of view is.
Quote: I have read discussions here that have convinced me that focal length is focal length regardless of sensor size.
True enough. The problem is that is a mistake to assume that shake has anything do to with focal length. It doesn't - it is a function of field of view only. It just so happens that we can use focal length as a stand in for field of view, if we first apply the crop factor to the focal length so we're comparing apples to apples in terms of field of view.
Quote: It seems to me that magnification is what reveals camera shake and that is a function of focal length.
Magnification is a huge red herring here, as it leads to enormous confusion when people try to sort out these issues ("but, but ... cropping n image doesn't magnify it, so in image produced on a crop sensor camera won't *really* be bigger than one on full frame..."). If you insist on thinking on those terms, the folks pointing out that the image from the smaller sensor has to be "magnified" more in order to view it at a given size than the image from the full frame sensor are correct.