The pointiness value as of present only takes into account the angle of verts to surrounding edges (with a slight blur) and does not take distance to such verts into account in any way, shape, or form. It does have the disadvantage as seen in the image, but it does make it very fast to calculate (even with millions of verts) and unlike a dirt shader, does not produce any additional time during a render.
Supposedly, it should be possible for a developer to base pointiness on the distance to angled vertices instead, but that may mean a notably longer calculation time in the render prep. stage.