All devices in a system generate noise which is propogated back into the mains and onto the rest of the kit connected to this mains loop. This noise gets into the rest of the system and can cause jitter and other nasties with cumulative degenerative affect. Digital devices seem particularly susceptible.
One of the things a good power cable will do is stop the noise from a device getting back into the mains, effectively isolating it from the rest of the kit in the system, as well as filtering any noise already present in the mains.
So it's not just about cleaning the incoming mains but ensuring system noise is not propogated.
When I test cables I always try to set up two systems in parallel so that I can immediately switch between them to hear differences, rather than relying on memory. It's not always possible of course, but is very worthwhile when available.
I use third-party power cables throughout my system.
Cheers,
Mark