The reason for this (at least from what I've heard) is that when you've got the credentials to get into an Ivy, the limiting factor for your success is "being able to complete your degree."
If you choose an "easier" school, your odds of completing a degree go up by a lot. You also stand a chance of being one of the best students there, further bolstering your transcript and opportunities for doing research while at the university.
Part of the problem is trying to work all this out at an age where you're not even allowed to vote, let alone buy a beer or a gun.
One of the surest things to aim for, in my opinion, is minimizing external debt carried afterwards, which for low income but high achieving students, may mean aiming at the very top, where full scholarships are available.
The studies I’ve seen contradict this. Students who are accepted to elite colleges but instead go to “lesser” schools do just as well as their Ivy counterparts. The exception is extremely poor students who do better by going to elite schools; researchers speculate that is due to networking effects. But that effect doesn’t generalize well like your comment implies.