Did the musicians perform better because they are naturally more sensitive to sounds, and thus more likely to study music? Or did their nervous systems change because they were exposed to music for more than a decade?
We're all a combination of nature and nurture

As a former h.s. math teacher/musician, I'd have to think from my observations that studying music rewires the brain. My husband (a h.s. band director) was an absolute failure at being able to show how to do an algebra problem, but he could see the answer, but could never show how he arrived at it. He was always sensitive to my needs, I just assumed it was because he was a Pisces and I was a Taurus.