> Is there evidence that a training class can overcome whatever combination of nature and nurture causes the discrepancy?

There is also the issue that the same behaviour is seen differently when coming from men and women. What is assertive in a man can be aggressive and offputting in a woman. Which means you'd have to have different kinds of courses for different genders, and it only starts there (more minority groups with less studies of what happens when they act the same as a white male). So, there is even more of a hurdle for potential training classes to overcome.