As I noted above, if you go to your lights and set them to raytraced shadows instead of depth cued, the problem disappears and the props render normally.  I have no idea why this is.  Nor why having a second object in the scene fixes it.

My two biggest concerns are this becoming a problem in anything I might do to sell in the future (I've got two furniture sets in the works now I was going to put in the marketplace here as my first entries).   Also, I don't like doing freebies that don't function 100% correctly, which is what I intend the shaving kit to be, a nice freebie.

Plus, not understanding why this happens, what causes it, etc. just plain annoys me.  I hate it when I can't figure something out.  LOL  

This shouldn't be a problem for freebies since I doubt anyone is going to be rendering a shaving brush or a straight razor entirely by itself... but still... it tasks me, it tasks me...