I've seen several papers that claim to "control for all factors" and still find a gender gap. What they usually mean is that they threw some additive factors in

I've seen several papers that claim to "control for all factors" and still find a gender gap. What they usually mean is that they threw some additive factors into a linear regression model of salary and found that according to that model, gender had an effect. What they notably don't do is control for all the intersections (which is the only thing that could actually prove that equally qualified and experienced women are paid less for exactly the same job). E.g. they'll say stuff like "controlling for field women are paid less, e.g. in medicine", while ignoring job titles, like the fact that doctors and nurses are both in medicine, but nurses are paid less and are more likely female.