Punt:
Both are equally important.
I have friends who are EXTREMELY involved parents – practically homeschooling their children in addition to the school’s education. But the kids didn’t test GATE. They perform as well or better, academically, than the GATE kids in their classes.
I have other friends who are busy, busy, busy. Nanny takes care of the kids – and english isn’t her first language. The kids test off the charts, but perform mediocre in school.
I think it’s got to be a combo of both.
I know that SDSU uses the Raven test – which tests abstract thinking (puzzle/problem solving rather than knowlege/facts/literacy). I’m not sure how parental involvement would improve scores other than an involved parent makes sure the child is well rested, well fed, and confident when they go to take the test.