First of all, who says that audiophiles look for brands with the lowest distortion specs? I have never heard anyone with an expensive system mention the distortion percentages of the equipment and some of the brands you mention have higher distortion ratings than much less expensive products. But as to the second part of your question, when you say "distorted" music, I assume you mean electric guitar and such, where the players deliberately add what is commonly called "distortion"?
In simplest terms, the goal of home audio is to reproduce what is on the recording. If the musician chose to produce a distorted tone, the system should reproduce it as it was recorded. If the home audio system has audible distortion, it will not reproduce the recorded sound accurately. BTW, I think you and many others consider distortion to be limited to noise or some objectionable sound. It may be, but in fact any alteration of the original sound is distortion. If you boost the bass in a way more pleasing to your ears, you are distorting the original sound.
In simplest terms, the goal of home audio is to reproduce what is on the recording. If the musician chose to produce a distorted tone, the system should reproduce it as it was recorded. If the home audio system has audible distortion, it will not reproduce the recorded sound accurately. BTW, I think you and many others consider distortion to be limited to noise or some objectionable sound. It may be, but in fact any alteration of the original sound is distortion. If you boost the bass in a way more pleasing to your ears, you are distorting the original sound.