I would suggest that their representation in the Ivies may demonstrate the social benefits of these schools rather than any academic benefit. In other words, the Ivies actively recruit from these schools. Therefore, there is a social capital advantage to attending them, rather than a purely human capital advantage to doing the coursework there.

So do they make a difference? Yes, but not simply because of the academic program, but because attending one gets you into a certain social world that includes the Ivies, which someone may not otherwise have access to.