[nshepperd]

Parent said "influence desired career paths", which is not the same as differences in performance. People choose a career path for many reasons besides ability, such as individual personality, ability in alternative jobs (note the quote in your first link which points out that "girls outperform their male counterparts on achievement tests in stereotypically feminine subject areas"), or even their experience being bullied in high school with regard to the job.

Furthermore, if you want to come to valid statistical conclusions about whether a discrepancy is due to a particular cause (and can't just do a RCT), it's not enough to just ignore plausible confounders until they are "provable". You need to systematically control for all possible confounders.