John,
One needs only to review what bad things a power cord is capable of to see that it can indeed make a difference.
I have never been talking about "bad" or broken components. I'm talking about a perfectly competent stock AC power cord that costs less than $5. There is no way to "improve" on that since a good power cord already does what it's supposed to perfectly well - deliver AC power efficiently to a device. Unless the load is 30 amps and the wire is 26 gauge it will work fine.
depending on it's construction, it can be the cause of hum.
How can one 3-wire cord have less hum than another? Wait, don't answer that. Here's the real issue:
The claims made by these snake oil vendors are based on magic, and on the premise that the improvements in clarity can be heard but not measured. This is pure hogwash. If one cord is able to deliver AC power "better" than another, then the improvement can be easily measured at the line level or speaker output connections. This is all I care about, and all I've been addressing.
Twist: The intent of a twist is to average out the magnetic field, so that any proximity loop ...
I'm also not considering badly shielded signal wires in proximity to an unshielded power cord picking up 60 Hz interference. The correct solution for that is move the wires, not waste $1,000 on a new power cord.