I uploaded the objects to Rapidshare.  It's only 13k but, I don't know how to embed text files in a post sooo.. Rapidshare it is.  If it runs out of downloads (maximum 10) then I will re-up it to my account at ShareCG.

http://rapidshare.com/files/197476310/Packed.rar.html

I included the mtl and generated texture-checker files in case there is something there which sheds light on the issue.  I think I got them all.  Their names don't match the .obj files which I have renamed to match the cylinders depicted in the above illustrations.

Check them out and experiment and/or doublecheck my results.  However, it'd be more useful if anyone could reproduce the same results using cylinders and Projected UVMaps of their own creation using a variety of different tools yet rendered in Poser.

Informed Criticism is important here.  "Why" this is occuring is of primary importance.  If you can shed light on it, falsify my findings, conclusions or reasoning, PLEASE do so!