The probability of that happening is greater if average test scores are higher. The "tiger parents" aren't just looking for schools that offer the best programs, they're also looking for schools that have less problematic students that disrupt the learning environment and would be bad influences on their kids.
The entire school isn't the friend pool, but your proximity of classmates.
If the class room sizes are roughly the same, probability of meeting two smart friends will be roughly the same.
Why must both schools have the same proportion of potential "smart friends"? Even if the school with better test grades somehow had the same proportion as all the other schools, all the tiger parents flocking to that school is going to change the proportion.
As a kid, to light the spark of a topic, i would say its more important that the other kids are genuinely passionate about something. Otherwise its just more homework.
Also you forget that the mean usually doesn't tell you a lot if you, like the poster mentioned, are mainly influenced by the immediate surroundings. If your kid is academically interested and already has good, smart friends, the gain of switching a better on average school might be negative.