Eldartford, that explanation is a fraction of what occurs when electricity passes through wire. In fact, I think next to proper gauge for the conductor, possibly the most important thing is the insulation.
Insulation can store energy and release it in non linear ways and various layers between the conductor (and outer jacket we see) can have a huge effect on sound.
A perfect example is Purist Audio power cables, which I am so fond of. The conductor is approximately 10 gauge and constructed with a mix of metals that have proven to provide excellent results.
My argument is NOT that Purist Audio's mix of metals is so proprietary that Audioquest or Shunyata (or whoever) cannot duplicate it, but rather the shielding, grounding and isolation from vibration, EMI and RF are of equal or greater importance.
Most of the time plugging in such a cable results in a blacker background with a more relaxed presentation and improved textures and resolution.
To understand this, you need to view the power cable as PART OF THE POWER SUPPLY rather than an extension of the Romex in the wall.
If you assume your AC power is perfect and your power supply in your stereo gear is immune to EVERY POSSIBLE contamination, then possibly the power cord will have less effect. However, there is still the issue of vibration.
For that reason, there is more than one audiophile manufacturer that addresses that problem in the construction of their power cables.
The energy drawn through the wires moves the wire vibrating it. A perfect example is caused by strobe lighting used in my photo business. The capacitors in the power packs sometimes causes the walls of buildings to "talk" back every time a burst of energy is drawn.
This power draw through the conduit is powerful enough to "bang" the conduit against the wall. I have had this happen hundreds of times over the last 30 years, even in high rise commercial properties.
In the last ten years I have seen almost no situations where a premium power cord did not help the equipment it was plugged into. Differences in design from manufacturer certainly provide an array of results, some of which I find desirable and some I do not.
To say that they effect in no way is absurd. In fact I hear differences between different brands of male wall plugs. Most often this manifests itself as tonal balance changes but sometimes as distortion. I assume this has to do with conductivity, vibration, and clamping action.
It's all important and cannot be measured with a volt ohm meter or resistance specifications.