Sure, larger socioeconomic problems will definitely turn up in statistics, because it turns out that being gifted heavily relies on parental model, and many many other things. Even a very motivated child will fail to partake in such a problem if he/she has serious problems at home, e.g. being beaten, having to work to support the family, etc.

But I feel it is very unfair, outright evil to take away an opportunity from gifted people (both from privileged families and a few from very bad families that would have been lifted up by said programs!! The aforementioned example could perhaps break the cycle and get a much much better life than any of his/her relatives) on the basis that the statistics on the enrolled will be biased. It is not the task of such a small-scale program to solve a huge, complex problem that probably can only be solved in decades if ever.