I think it really depends on the kid and on the school. It sounds like the school you have in mind hits a lot of the qualities to look for when looking for a good fit. I have a kid with stats that were the in the 75th or above percentile for most selective schools. On her list were some very selective schools and also some that were less selective, but seemed like good fits in many other areas including student body, programs offered and part of the country.
One thing we did talk about when looking at schools was that her high ACT score is not a measure of her intelligence, but more a measure of her college readiness. If she were in college classes where the average student was still learning the things she has already had access to in her rigorous high school, she might be bored, and when she is bored, she has a tendency to check out. The private high school she goes to now is very selective, and although there are aspects she has disliked about that such as competitiveness and some stress, she has also appreciated having 4 years surrounded by kids who really value intelligence instead of downplaying or being embarrassed by it, and who can all fully engage in the strong curriculum. The students she goes to school with have really helped her rise as a learner - they all bring so much to the table.