Given that I've got a rather nice chunk of cash (buy-a-really-nice-car nice) from a settlement in a pay gap lawsuit, there's at least existence proof that a pay gap exists occasionally to the extent a judge will believe it does. I'd consider looking at the actual data instead of blanket-dismissing via generic questions.

Further, given that the AEI has a very strong incentive to lie a pay gap away, I'd at least suggest consulting additional resources.