Quote - numbers 6 7 8 in your zip.
and I DID put a checker texture on. that's how I saw each one was flawed in the mapping.

Yes, the mapping is flawed if you were going to put a texture on it.  But, that doesn't make a difference in regards to this particular artifact.  There is no texture here to be distorted.

What's more, as seen in illustration 9 (IIRC) you can have even worse UVMapping and as long as it is done with a Planar Projection, that particular artifact will not appear.

These UVMaps were not done for texturing purposes.  The quality of the UVMap in terms of applicability for a photographic texture does not appear to matter as far as this artifact is concerned.  It is the Projection mode that seems to be having some sort of effect.

"Could" distorted UVMaps have an issue?  Maybe.  But, all the ones I have tried so far do not yield any artifacts as Illustration 9 (IIRC that is the correct number) shows.  It has a badly done UVMap but shows no "ripping" artifacts at all.