>> But stars (and gas clouds) orbiting in a disk are essentially always "near the edge" of the disk (that is, the disk defined as matter interior to the orbit in question), so the approximation is usually pretty good.

Not sure we're on the same page. For a star orbiting at radius r on a disk of radius R, some folks will lump all mass inside r into a point and apply keplers laws. They will reject all the mass between r and R because of the same surface integral theorems. The problem is that neither of those assumptions are anywhere near correct. The pull from the interior <r mass is not the same as though it were a point, and the pull from the outer mass >r is very much non-zero. For an example using electric charge instead of gravity:

http://www.phys.uri.edu/gerhard/PHY204/tsl34.pdf

Note that the field is non-zero at most places inside the ring, however it would be zero over the entire volume if it were a spherical distribution.