Actually, there is a sense in which we CAN tell you what you can hear, or what you can't. It's not totally subjective; or at any rate it doesn't have to be. (I agree that comparing anecdotal experience is not conclusive.) If you can hear the kind of difference we're talking about, you can prove it under proper testing conditions; if you can't prove it, you can't be said with any certainty to be capable of hearing it. It doesn't even require scopes or anything like that.
Set up a properly blinded ABX test listening test between the two power cords. Then do a comparative listening test, for as long as you like. If, under these proper test conditions, you can repeatedly, reliably, and reproducibly distinguish between the two with a frequency significantly greater than mere chance would allow--you don't even have to get it right every single time--then it's reasonable to think that you can in fact hear the difference. If you can't do this, then it's fair to say that you can't hear the difference, no matter how sure you are that you can.
If you failed this test, yet still claimed you can hear the difference, then I could with justice say that you actually can't, thereby "telling you what you can hear."
It's true that none of us can hear exactly what someone else hears. But we can, at least in some cases, discover something about whether other people can hear certain things they claim to hear.