Regarding the name, he was referring to you calling it a "ground cable." Those are used to connect a component to ground, and that wouldn't cause the issues that you're having. I'm assuming now that you're referring to a power cord.
Cables can have poor connections at the terminals, which might be more prone to showing symptoms when the sub is moving more (at moderate to high levels). So, it's not out of the realm of possibility that a cable is causing this.
You could swap out both the RCA cable that you are using to connect the receiver to the sub (which is a more likely cable to have issues), as well as the power cord, to see if that clears it up. It might, it might not. The sub may very well have been at Goodwill because of this issue.