Don't know about Page and Brin, but according to the Netflix documentary Gates won state-level math Olympiad at a level three grades higher than his own. So he wasn't a modal child. You can't draw any conclusions from that about education at scale.
As someone who participated in many academic competitions as a child, the winners were consistently weighted 9:1 private:public.
> https://doi.org/10.1126/science.1238041
That article doesn't seem relevant. 'Poverty impedes cognitive function' is entirely compatible with 'IQ is highly correlated with wealth and is also highly heritable', and with the claim that private school can't make a genius out of a kid who lacks an extremely high IQ.
edit: maybe I misunderstood, and you only were only pointing out that some potential-genius kids have that potential stifled by poverty. But that doesn't seem to be the original point of disagreement.
https://www.researchgate.net/publication/259207757_Comment_o...
On the first page, the breakdown is 23 kids from public schools, 7 kids from private schools, 4 kids listing some sort of math circle / whatever Arateem is, 5 kids listing universities (home schooled/taking uni courses? No idea). Possibly a few of the private school kids are on scholarship. The 7 kids go to 4 schools.