I don't think anyone serious is claiming that the only reason these firms underpay their people is because of high CEO wages.
The place where we should really be seeking out evidence is whether having a high-paid CEO actually directly increases profitability/revenue. There's at least some evidence this is not true: 12. A similar question is whether workers earning low wages perform as well as workers paid prevailing or better wages.
What this kind of reporting highlights is just how wasteful and immoral it is for the executives to be cutting themselves such obscenely huge paychecks while operating a low-wage firm. It's evil. And on top of being evil, it's probably bad for business. Even if the "bad for business" part is purely that the executive high wages themselves are a waste of money.