Evidence that Gary Becker is correct that minimum wage reduces the cost of discrimination

This post reports a study that finds US firms are hiring women at lower wages than equally qualified (or even less qualified) men. Hiring women gives the US firms a cost advantage. As other firms mimic the US firms to keep up, the increase in demand for women and the decrease in demand for men will reduce the disparity in wages. 

If minimum wage forced the US firms to pay the same wages to men as women, the US firm would not have an incentive to hire women over men and could not set in motion changes in demand that => less disparity in wages.