You use the term "self shadowing" which can have several definitions and causes. Among the causes for artifacts (a more general term) is the closeness of depth values between the shadow map and the scene depth. That closeness can result from several factors - one of which is the difference between shadow map texels and scene pixels. That is, the shadow map characterizes a texel at a single depth. From the scene point of view, that texel may be sampled for several pixels to be rendered. If the scene depth varies over those pixels (particularly along edges or faces with high slope values with respect to the view direction), those depths will all be compared to the same depth in the shadow map. EDIT: that is, when pixels are rendered close to the edge of an object, some of the pixels are at "background" depth. When the edge of the object is rendered adjacent to a "background" pixel, the depth decreases dramatically. However, both the "background" pixels and the closer object pixels may all be at the same texel location in the shadow map.

The closer an object is to the near-plane in a scene, the more pixels are rendered, and the more likely a single shadow map texel will be sampled for multiple pixels. It may be that by scaling the mesh, you're reducing the number of pixels in the scene that are compared to a single texel.