That is historically true, but it's worth noting that there have been two intervening events since the heyday of that talking point.
2. Illinois is not the prestige-humping institution it once was. That's a new leadership thing, that's a state politics thing, that's a modern realities of higher education thing, it's a culture of the college admissions process thing, it's a variety of reasons that the days of Nancy Cantor being desperate to cosplay that we're Michigan are over.
Doesn't mean we still not might turn down a kid that another Big Ten school would take, but it's not what it was.