This is a neat story, and Feynman is of course a genius and raconteur of the first order. But it sounds too good to be really true, and Feynman admits at the end that the transcript that his narrative does not match the transcript; in other words, that it's partly fiction.

Regarding men and feminism, this quote is probably very apt:

"The first principle is that you must not fool yourself—and you are the easiest person to fool."