Very loosely, speakers are low impedance, require high current and low voltage. Headphones are high(er) impedance, require low(er) current and higher voltage. Consequently, the types of wire used for each is different, though using 18AWG wire, which is just about speaker cable or power cable (!), for headphones, is pretty funny. The more current, the thicker the wire required, which is why power lines are relatively thick. It's more likely that large voltage swings would be affected by the quality of audio components, and less so, say, speaker cable that carries a large current.
The problem with this kind of discussion on here is that it's pretty far removed from science, involved in proposing theories, methodologies of testing, possible errors, performing experiments and writing them up correctly, but just people arguing about things they read online and taking sides because it suites their desire to be right, not to find out or know the truth. Unfortunately and presumably as a result, the people who are heavily involved in actual DBT testing and whatnot don't seem to be posting any more because of this.