The problem is that the experiment likely didn't prove it.

Yes, it is true that there are massive problems in failure to replicate in psychology, not to mention bad statistics etc. However, a single experiment is still evidence in favour.

Then the reporter overstate the results

Actually, the reporter understated the results, for instance by including this quote from an academic who disgrees:

“There is absolutely no reason to expect that women's hormones affect how they vote any more than there is a reason to suggest that variations in testosterone levels are responsible for variations in the debate performances of Obama and Romney,” said Susan Carroll, professor of political science and women's and gender studies at Rutgers University, in an e-mail.

Carroll sees the research as following in the tradition of the “long and troubling history of using women's hormones as an excuse to exclude them from politics and other societal opportunities.”

Thing is, Prof. Carroll is not a neuroscientist. So what gives her the right to tell neuroscientists that they are wrong about neuroscience?