Yes, technically, speaking, light ray is constant.
When I said that the shaking of the light ray, I'm speaking on the relative terms whereby the camera sensor is seen as a constant on which the light ray falls on. When the camera shakes, the position on which the light rays falls on the sensor will change.
The shake is said to be "magnified" not because of the "magnification" factor of a longer focal length per se but because of the longer (physical or otherwise) distance between the optical centre of the lens and the image sensor (i.e. focal length). Don't forget that magnification factor not only depends on focal length but also shooting distance.
An example would explain this :
You use a 90mm lens and you shoot from 1.8m away from the subject, your magnification factor is therefore 1/19 and a 684mm (19x36mm) subject would fall on the full width of a full frame (36mm width).
Now if you use a 180mm lens and you shoot from 3.6m away, your magnification factor will also be 1/19 and the 684mm (19x36mm) subject will also occupy the full width of the full frame.
Magnification factors are the same for both cases but the shutter speeds to avoid hand shake are different because of a difference in focal length (90mm vs 180mm in this case).
Related to the above, it is a common misconception that handshake is magnified because of the higher magnification factor of a longer focal length. Another example will explain : If you now shoot the 684mm subject from 7.2m away (instead of 3.6m away) with your 180mm lens, you magnification factor will become 1/39 and your 684mm subject will be only 17.54mm (instead of 36mm) on your image sensor. Now, your magnification factor is different (1/39 now vs 1/19 earlier) and your subject is now much smaller in the frame than previously. Do you now change your handheld shutter speed? Clearly, even the magnification is clearly smaller at 1/39 now, the guideline remains at 1/focal length = 1/180 regardless of whether you're shooting from 3.6m or 7.2m away (i.e. whether magnification is 1/39 or 1/19).
Those who are familiar with Tennis knows how a ball deviates from an intended spot on the court depends on 2 main factors : 1) the angle of deviation from the intended direction, 2) the distance the ball travels (which is a result of a few factors).
In photographic terms, the 2 factors correspond to (1) hand/camera shake, (2) focal length.
Given the same angle of deviation in direction, the deviation from the intended spot on the court depends on the distance it travels.
Draw a diagram yourself and you can easily see why. Draw a horizontal straight line and then draw another straight line which is 1 degree angle deviation above or below of it at the starting point. We can easily see that the further away it is from the starting point, the greater the distance between the 2 lines.
The starting point is the optical centre of the lens while the distance from the starting point to the ending point is the focal length.
For the same amount of camera shake, the greater the focal length means the greater the light ray will change from its original spot on the sensor.
It's less of an issue with short focal lengths simply because shorter focal length means shorter distance (physical or virtual as in mirror lenses) between optical centre and the image sensor.... which means the spot on which light ray falls on the sensor will change little when an extremely short focal length is used.
At the end of the day, it is the focal length (i.e. distance between the optical centre of the lens and the image sensor) that ultimately determines how any handshake will be translated to a shift of the physical image on the sensor.
If the shutter closes fast enough, then any shift of the physical image on the sensor will be very limited and no image blur is apparently recorded.
FOV due to different sensor size is irrelevant because it does not affect how much the physical image shift on the sensor due to shake.
Hopes the above clarify some misunderstanding and hopefully don't mislead. At the end of the day, what matters is what you are able to handhold at and not what websites say.
Just like previously, I will refrain from arguing further about the handheld guideline and will let people believe in what they want to believe in. Otherwise, there will be too many things to explain (now some may wonder how to get the magnification factors calculated above. And no, I didn't get the numbers from websites but calculated them myself using a simple logic/formula. The numbers can easily be verified. Slight differences in the numbers can be attributed to the different definitions of shooting distance and have no impact on the validity of the above arguments.).
As said before, to test the effectiveness of the IS, a person needs to compare a picture taken with IS with the same picture taken without IS, and not against a shutter speed based on a guideline for a normal pair of steady hands.
Here's another handheld shot without any image stabiliser :
Actual focal length : 8.9mm
35mm format equivalent : 35mm
Shutter speed : 1/8 (motion blur clearly seen)
