The "obvious evidence to the contrary" was the math gender gap, which was very real at the time. If you actually read the story, it's quite clear that Feynman is telling the story at his own expense (showing how wrong he had been about girls + math). There's no question he was sexist, but see _debug_ and blackguardx's tandem quote to see that he regarded them as equals mentally: http://news.ycombinator.com/item?id=1197382
I did read the whole article, but did not get the impression that it was meant to be a joke at his expense. That's just not supported by the text. The most he's willing to say is that "if it is done in the right way, you may be able to get something out of it [the female mind]." Hardly a U-turn.
Also, the quote you referenced does absolutely nothing to show that RF regarded women as his mental equals. It just shows that he sometimes explained stuff to them -- not surprising, given that he presumably had some female students/colleagues.
In any case, whatever the merits of Feynman's position at the time, I'm bemused that anyone could find his views on this topic quoteworthy.
Although, in Feynman's defence, practically no-one that he met in his life was his intellectual equal, man or woman... I think it's just that he was more willing to actually say that for women, whereas he obviously felt a social need to keep that thought to himself when it concerned men.
