My point, which remains valid even if I had misunderstood yours, is that yes, in many cases women do make less, on average, than men with the same position. For the type of positions where wages are open to negotiation rather than rigidly determined by law or company-wide rules, that is. So yes, it has to do with negotiation - those women being less likely to assertively request a raise, less likely to drive a hard bargain or threaten to quit if a raise is not forthcoming. But it's not that simple, it's not that they are just worse at negotiating - it also has to do with society's expectations of how women should behave, which in many cases simply don't allow them to play the game as hard as men without suffering major negative consequences because they are perceived as bitchy, hysterical, or the like.
In order to make assessments of whether they are worse at negotiating or not, you'd have to be able to make fair, blind comparisons where women and men are held to the same social standards during the whole process.
What I was trying to say is that society has moved past the 'can we trust women with responsibility' question a long time ago and considers it very much settled. And if you're asking the more fervent kind of feminists, they'd probably tell you that the real question is if men can be trusted with responsibility.

Thing is, of course there are real differences between the average man and the average woman, and there's a reason behind the stereotypes and the different expectations, but on the other hand both genders also cover such a wide range of personalities that very few of those differences are truly universal (and none at all once you start looking at transgender people), which means it's still important to continue the struggle for a society that doesn't impose the norm of the average on everyone.
And beyond that, I don't think we've really reached the point where women are genuinely what one might call 'separate but equal' just yet. Unless perhaps you use the term in its historical sense including the scare quotes around 'equal'.
The scientific accomplishments of today's society do allow one to counteract such biological differences, though, with contraception largely invalidating that argument. And further down the line, while basic biology permits only the mother to give birth and breastfeed, there's no biological reason why the father couldn't handle most or indeed all other aspects of raising children. Very likely the large majority of couples wouldn't even desire such a role-reversal, but some would, and why should society frown on that? And more might desire it if there was indeed more tolerance for it.
That's a large part of the explanation to be sure, but not the whole of it - and they are intertwined, in the sense that over the long term women would start making difference lifestyle choices if society's views on women and gender roles evolved, and they could make higher wages.
It sounds plausible enough that that would be the case, but I'd have to agree with you that it's not something really worth bitching about - those women for whom the salesman's generalized assumption is appropriate, well, you can't blame him for trying to make more money, and those for whom it's not appropriate can just walk away.