You’re welcome to try and come up with evidence that political correctness does not trump all other selection criteria, but I think you’d be a fool to try.
I made no such claim and I never would. I'd never attempt to prove a negative either.
You, however, did write:
...it is statistically far less likely that a woman could be as good at this than that a woman would be selected based on a PC need for a woman to be selected.
Your claim, your proof.
Requiring proof of the obvious is an argumentative tactic commonly used by the desperate. You’ll not be wasting my time with your political masturbation.