I'm suggesting that the factors you mention that were accounted for - such as experience - and that generate the higher income for men, are considered by some to be, themselves, subject to bias. Under that rubric, accounting for such things as experience to explain wage disparity is simply shifting the objection to the structure of how we determine which factors should have input into the equation. There is just as much choice in deciding that time-in-grade should justify a higher wage as any other attribute. If we artificially select attributes which women do not share in equal proportion with men, then we get the same result we might get with flagrant discrimination.
There's a parallel argument being made against including an arrest record as a bar to employment. Blacks are arrested more often (per capita) than whites. Using what appears to be a racially-neutral attribute (arrest record) then has the effect of limiting opportunities for blacks. So too might other, gender-neutral qualifications adversely impact wage rates for women.
This framing makes the original "wage gap" relevant again, because saying, "if we factor in these things reduces the wage gap" is a tautology - in effect, saying, "If we remove these factors which unfairly reduce wages for women, wages are not reduced as much for women." A tautology instead of an explanation.
