Almost in-total, the "old boys" applicants are not under-qualified. When compared to almost any kid that attended lesser secondary schools than the privileged kid attended, on average.
These kids have almost always proven themselves in elite educational environments. Most of those who skate by in such environments don't go Ivy. They will instead attend one of the many more numerous elite Liberal Arts colleges that most others ignore but that carry almost equivalent cache.
There are no Stuyvesant valedictorians missing Ivy admissions. In the same vein, there are plenty of prep school kids who do. I've only rarely seen underqualified kids go Ivy, and the only one that I can actually think of was a poor kid.
Today, Ivy's are skipping qualified lesser privileged kids for diversity. In eliminating the SAT/ACT, they are essentially gambling that their reputation rather than their student body will continue to qualify them as Elite. Over time, I have doubts. The curriculums will have to be adjusted so as to avoid the pall of racism or classism that will occur when wildly divergent grades become apparent.