Focal lengths & crop multipliers

Forgive the question I'm about to ask, because it may be obvious to some (or most), but it isn't clear to me:

For cameras other than FF (DX, M4/3, Nikon CX, etc.), why is the focal length of the lens multiplied by the crop factor to obtain an "equivalent" focal length, IF the lens in question is designed specifically for use with that particular camera (like the Nikon 1 system lenses)? After all, these lenses weren't plucked from the "DX" basket or the "FF" basket; they were designed specifically for use with the Nikon 1's body and CX sensor.

I understand the methodology when using a "FF" lens on a "DX" body, but I don't see the relavence when the lens is designed specifically for a given body (family of camera bodies) & sensor.

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Drew