Ok, I asked a reputable audio cable manufacturer about some of these questions because I find this stuff highly amusing intellectually.
When asked about this directionality, I found it interesting to note explicitly that the company's representative believed that no cable mfg had a scientific measurement of directionality but that they must listen to a sample from each bundle of cable in order to ascertain its directionality. Thus this is a highly human process that is subject to plenty of error (arguably moreso than a more controllable process) and would affect entire stocks of cable manufactured at a particular time.
The company rep suspected that the directionality thus comes from the grain and crystal structure (sic) of the conductor material itself, and is a quality inherent in the conductor prior to burn-in.
So the natural question to follow is regarding burn-in. Of course he wouldn't be much of a rep if he denied burn-in, I suspect, and rightly so he believes that the interplay of energy loss from the conductor to the dielectric insulation and the subsequent either loss as heat or reflection back onto the conductor is the primary effect of burn-in. Over time this energy exchange and the subsequent delay of absorption and reflection settles down, to a perceivably audible level.
How much of this do I believe? And let me just state that this is a matter of belief in the sense that I don't take any of this stuff at face value, yet I thought it could contribute to the discussion. Well, I certainly think it's plausible.
My materials science is however admittedly rusty, and I'd love to hear some more knowledgeable positions on whether or not the idea of asymmetry regarding conductor grain sounds like a reasonable idea.