Again I have no direct experience yet with boarding schools, but I would agree that at college prep high schools in general, there is very little you can do to entirely keep peers from competing with each other, including as to college admissions. That’s just too fundamental to our sort of socioeconomic system, and they are going to be learning about that system (sometimes arguably mislearning) from each other, mass media, social media, and so on.
But I do think you can at least ask the other important adults in their lives to have values broadly consistent with your own. And I also think you can at least shade the peer mix in your preferred direction by understanding, as well as you can, how other kids/families are picking their schools. You can then choose the schools where the most common perceptions of institutional value-added are most closely aligned with your own values.