You don't need to know the mechanism to prove that it "supports the theory that there is a difference in brain organization". If there wasn't a difference, it wouldn't be able to find it.
>It's just as likely some confounding thing that's not causally based on the brain
Given that it does it's identification by looking at the brain, whatever the cause is, it is ALSO manifested as a "difference in brain organization".
>That said I'm surprised that we can't tell men and women apart from the brain.
Who said we can't? The article points to that we can.
And there are other brain attributes besides organization we can use to tell them apart, the biggest being size, including size of certain structures.