Ah, I thought you were making some special argument about stars orbiting with very tilted orbits or something like that.

Yes, the orbits within the inner part of a galaxy don't follow a Keplerian curve. However, at large radii most of the visible matter is well inside the orbit and very little is outside (galaxies are quite centrally concentrated), so the rotation curve should approach the Keplerian limit as you go to larger and larger radii. The fact that it doesn't is one of the primary pieces of evidence for dark matter in galaxies (though not the only one).

(I'm not sure why you linked to that slide, since it's not calculating the field in the plane of the ring, nor is it dealing with a continuous charge distribution. Regardless, you'll note that E_x goes to 1/x^2 for x >> a, which is a "Keplerian" limit.)