Please correct me if I'm wrong but...

[Jon Ruyle]

I was thinking of the situation where you simply move the lens from a FF to a crop-sensor camera, without changing distance to subject.

But that's a silly comparison, because you're getting a totally different picture. The point of "effective" f number and "effective" focal length is that you get the same picture on crop with an effective fl and f ratio as you would on full frame with a real fl and f ratio. Same subject distance, same perspective, same diffraction, same everything. (Well, not really, but that's a different story)

the DOF only depends on aperture diameter (given a subject's distance)

True enough.

so one can't always make the assumption that the photographer will change the distance to subject

I agree. Photogrpahers can be crazy. I wouldn't assume anything about what they might do.