while I agree, that very smart children can be victims of their childhoods, not everyone can prep their way into MIT. that is why Harvard and Yale are more prestigious, its more associated with the powerful, not purely the most academically inclined.
To be clear I grew up fairly poor myself with no support system, but not that bad with violence, just trailer park poor, you can tell smart children at a very young age, kindergarten it will be obvious if a student is mathematically gifted(for whatever that is worth, it is certainly not the end all be all indicator of future success).
my point is that MIT will have a higher percentage of mathematically gifted students, because it isn't something that can be prepped for.
I guess I would be curious on how much a difference it really is , if you could completely control for environment, but even then the difference still exists.