I have given you a concrete example of a power cable radiating EMI from a subwoofer. The EMI was sufficient to take out my TV reception, which of course is a low-level digital signal. This is entirely reproducible, and was solved by modifying the cable by adding two ferrite chokes. Untamed, this EMI would feed into any other connected component which just might affect its performance?
As a Cambridge-trained physicist, my natural inclination is to disbelieve odd claims. However, reports of RFI affecting sound quality have been around for decades, so maybe there is some real phenomenon at play. Back then, everybody thought it was from the mains, so it seemed non-sensical that the last six feet could make a difference. Much more recently, our own components have come under suspicion, especially those with electrically noisy digital circuits, or switched mode power supplies.
Rather than dismiss what people claim to hear, I would prefer to try to understand what they are reporting. It may be psychobabble, or it may be a real phenomenon we don't fully understand yet.
Do I personally think changing a power cord can move your virtual listening position? Never in a million years, but every good scientist should keep an open mind. I also deplore the reluctance to do A / B testing, especially on something as easy to swap over as a power cord.