How may a simple "Power Cable" change, improve an audio system?

How? How can just a power cable change improve the sound of ANYTHING? 
  Damned if I know. I have my own theories. But as of right now they are very simply just that, "Theories".
And I am a skeptic on this, "At least to a point". 
  Yes, I believe that;
A new, shiny power cable, simply designed to spec. "According to the NEC". And with basic shielding, twist and good terminations along with appropriate insulation "should" in my mind sound better than the ratty old power cable that came with "whatever component". But that's not always the case in my experience. Sometimes the new power cable seems to make no difference at all. And beyond that? I simply know that it "can" be an improvement.
  I do understand that many here believe that anything to do with, "High-end Power Cabling" is just, "Snake Oil" for sale. I used to think the same. But things like this that I am about to report to you just keep happening to me....
  Last Saturday at 7:00pm I was at the "Capital Audiofest" in Washington D.C. And that evening there had been arranged a bit of music "Live", for those of us that were still there at 9:00pm (I "think", it had been a long day)..  I happened to walk in early as the band was just doodling around after just setting up for the gig. They sounded really good and I decided to just hang-out until they played. as the band was going through the set-up and about fifteen of us on-lookers were just talking amongst ourselves between practice songs. A fellow whom I do not know stuck his "head" in the room and yelled someone's name. The bands leader stopped and looked around. The "Head", said; "Plug your amp in with this and it will sound better"! The "Head", then disappeared as quickly at it had appeared, never to be seen again!, "By me at least".
 There were a few scoff's that I heard. A few chuckles about a power cable, "Making an amp sound better"!?
  Then the band leader shrugged his shoulders. He laughed a bit too as he remarked and joked, "Well ok then, A power cable that will make my amp sound better huh"!? He then bent and swapped out the old cable for the "New" one.
     The band leader then played what sounded like the beginning of a song for about 5 seconds. He stopped, "With a bewildered look on his face and looked around as if confused" and then began playing again. After another ten seconds or so he stopped playing again. He looked around the room "Again", with a questioning look on his face. In fact I noticed several people with odd looks. A  couple of them looked simply, "Dumbstruck". A few others had smiles. But honestly? The bandmates looked mainly confused! Then everyone seemed to chime in at once. "Sounds great!", "Sounds better", I heard among other comments but all seemed positive. 
And I have to admit, there was a difference. To me? Not a small or slight difference. A absolutely HUGE difference! Both more open and dynamic it had sounded. Larger and more alive, with more detail too! 
And I have to say, as I "was" sitting right there in the second row about twenty feet from his amp. NOTHING had been changed except for the cable, A two second cable change on the rear of the amp. That was all!
    The band seemed to be having difficulty with this. For about five seconds! Then someone tried to basically tell them that "Yes, The power cable can indeed make you sound better". 
Just as the, "Head", had said!
And the band played on!
 Has anyone else had a similar experience?
Even I was very surprised that the small, "Maybe a 10 watt amp with a ten inch driver". Could have such a major improvement with JUST a power cable change. I never did find out what the power cable make or model was but I will. I talked to the band leader dude and offered to send him a IEC inlet of good quality as he promised me he would swap that out on his amp and let me know of any differences there "If any".
            Thanks in advance for all whom respond!