I never responded to you but I still stand by what I said for a variety of reasons >.>
1) I never said control for "all" variables, I said control for some, and I listed which ones. I recall that the paper in question listed justifications as well.
2) I never said to "ignore the other part of the gap for no reason". This was in the context of the claim that there is a certain gap explicitly caused by refusing to pay women an equal wage. It does not matter that the academic argument is more sophisticated because the conventional argument in popular culture is not. It intentionally oversimplifies a phenomenon which is in itself disinguenous. This is not a straw man because I can point out many examples of politicians and pundits making this claim, which inevitably filters into the popular discourse.
3) You're right, I have not taken an econometrics course.
My training is in statistics, not economics.