Some posters are getting things mixed up. Two halves of the same coin maybe, but not the same.
The shutter speed = focal length thing is not a rule, but a rule of thumb, a rough guide*. Images do not magically become sharp as soon as you achieve the prescribed ratio, they merely become 'acceptably sharp'. There is always some camera shake with a hand-held picture, but it gets progressively reduced with faster shutter speeds until it's 'acceptable'. What is 'acceptable'? Well, your guess is as good as mine but this rule of thumb goes back a long way, to when a 10x8in print from 35mm film was a good size enlargement. Today's standards are higher, and this is where pixel count comes in - the closer you look, the more critical you are and the higher your required standard of sharpness, the higher the shutter speed needs to be.
But the rule of thumb as we commonly use it is unrelated to pixels - it's simply about magnification. And in that sense, it holds good, regardless. Say you get a good sharp image at 1/100sec with a 100mm lens, then with a 200mm lens you'll need 1/200sec to counterbalance the increased magnification of the longer focal length, a 400mm lens needs 1/400sec and so on. Not everyone can hand-hold to the same standard, and what do you call acceptably sharp? Everyone should do their own tests, and output the images to their usual standard, and draw up their own set of guide lines.
If you do that, and shoot a sequence of pictures around your personal limit, you will not see them all equally blurred. Some will be sharp, some will be acceptable, some not. The point here is, when you're up against it and fighting to get a sharp result, there is safety in numbers. Shoot a sequence with the camera in continuous drive mode, and there's a very good chance at least one will be good. Your chances of success are dramatically increased.
*The fact that the shutter speed = focal length rule of thumb works directly with full-frame (35mm film) cameras is pure coincidence. For all other formats, a conversion factor, eg crop-factor, must be applied.