Ehhh you're really gonna need to show me this study, including detailed descriptions of the male and female cohorts showing that every male and female pair in the study are exactly the same age, have the same amount of experience, exact same education level, and work for the same company. Otherwise you can't really claim that the only difference is gender, now can you?

The problem is, you can't come up with such a study. Furthermore, the idea that companies are paying women with "exactly the same" skills as men in "exactly the same" positions up to 20% less doesn't make any sense at all. Why would I ever hire a man in that case? I'd rather save 20% off the top. And if I had no choice but to hire a man, why would I pay 20% over the market rate? And how is it that this conspiracy to pay women less exists in every company, in every industry, in every country in the world?