If the cables aren't shielded then you're running a couple of antennas that will be highly sensitive to external interference so small changes in position will result in differences in quality (like when you unplug them and turn them around). If you flip a coin three times and it comes up heads then you might think that the coin has a bias toward landing tails side down.
The impact of the interconnect on sound reproduction can be down to the capacitance, inductance, shielding and quality of contact at each end. There is a possibility that the interconnects find a better contact one way round rather than the other so that might be something else to consider.
From all of this discussion I think the impact of running unshielded interconnects has monumentally more impact than easing the flow of electrons through a conductor. I prefer to use balanced interconnects of a modest cost that cancel out most of that interference at the receiving end... and that's what recording and mastering studios prefer to do as well.