Fair enough, Twl. First of all, let me say that you are not under attack, and that I think you should be free to decide on whatever products you want to buy based on whatever comparisons you choose to make.
Second, let's be clear about what science is, and is not. No one claims it to be the final truth. It is no more than the best explanation for something, based on everything we know to date.
Third, there are a number of different sciences at play here. Yes there's electrical engineering, and the physics that underlies it. There's also biology (since part of your "system" is your ears) and experimental psychology, which is also a science and operates under the same empirical rules as physics.
I don't know enough EE to say for certain that power cords can never affect the sound. I suspect, but cannot prove, that when they do, there is probably something wrong somewhere else in the system, since it's not terribly difficult or expensive to build a power supply that can handle the normal quirks of residential electric service.
No one claims that, "If we can't measure it, it must be your imagination." But the tendency of people to hear differences between things which are demonstrably identical is a scientifically validated phenomenon. So if you compare two power cords (without the kinds of scientific controls that those who study human hearing use) and conclude that they sound different, the best you can say scientifically is that there MIGHT be an electrical reason, or you MIGHT be falling victim to this "placebo effect."
Of course, the more plausible the electrical explanation you have for something, the less likely it's the placebo effect. The lack of a good electrical explanation (absent, say, some known problem with a power supply) is what leads some of us to suspect that the placebo effect is at work here.
Finally, let me say that "falling victim to the placebo effect" is not a bad thing. It's normal, and no one is immune. (Including me. I once witnessed a demonstration of the infamous green pen effect, and damned if I didn't hear a difference. But under the circumstances in which I heard it, the placebo effect--or a judicious nudge of the volume knob by the salesman who was doing the demonstration--was the most plausible explanation.)
I don't expect you to agree with everything I've written here, so I suppose we'll just have to agree to disagree. But I hope I've made it a little clearer where I and some others are coming from, and maybe that'll help keep the sniping to a minimum, which is something we can all agree on.