Yes, that's true, it's the 'effective' focal length that is the key figure, but actually, it's just a shorthand for the magnification - that's the thing which really matters.
Folks assume that since the focal length doesn't change when you change formats, that the hand-holding rule isn't affected. But it is, and as I said above, the fact that shutter speed and focal length just happen to work out the same with full frame, is pure coincidence.
By the same token, the hand-holding rule also changes when you enlarge an image, because you enlarge the amount of blur within it. It's a very rough rule, and actually I think it's pretty marginal. It should certainly be regarded as a minimim standard, as while a shorter shutter speed obviously reduces the affect of camera shake, it doesn't eliminate it. People should do their own tests to see where their individual limits lie. It also varies a lot according to how you hold the camera, leaning against a wall, down on one knee and stretching uncomfortably, elbows giving good support, that sort of thing.
To take an extreme example, you wouldn't try and hand-hold a compact with a 100mm lens at 1/100sec. An average compact has about a 5x crop factor and 100mm is a massive lens on one of those, about 500mm equivalent in terms of field of view, relative to full frame. So 1/500sec minimum.
Then there's IS of course

Absolutely fantastic invention IMHO