Yes! It's not that somebody said, "hey, we can pay this person less simply because they are a woman." It's that the employee themselves may have negotiated for more.
Correlation is NOT causation.
Correlation is NOT causation.
I think, given what I've seen so far, women are given less leverage to start with, they are subject to the chilling effects of gender biases, and they are discouraged from negotiating more often than not.
Sure, a woman can overcome these obstacles, but she shouldn't have these extra obstacles in the first place. The "pay gap" is almost certainly not due to managers thinking "oo I'll pay her less because she's a woman," but it is still indicative of some (more complex) gender inequality.
What you are saying might be true if most hiring was done by CEOs and not department managers.