Barry states my own thoughts well. I try to frame a situation like this first in terms of the child's educational needs: Where will his learning flourish? Next, I would think with the parents about psycho-social needs and religious/spiritual/community belonging needs? Can they get the whole package in the competing school? Then that's where they should go. If the learning piece is best in a non-Jewish setting, how will they provide Jewish life and learning? Is there any way we could help?
I do think that a Jewish school can be a resource for thinking through these issues for any family who inquires, whether or not they choose to come. In this way, we can serve the entire community, not just the families of students who matriculate with us. The wealthy family might be able to help us expand our offerings to reach a greater variety of students. There's nothing wrong with coming back to them later to request help in serving future students; they will understand the need better than most people.