This is an instance where statistics can be misleading.
For illustrative purposes, let’s just say Williams has 500 grads per year and Michigan has 7,500. It’s reasonable for a graduate program to suggest that their cohorts are composed of a diverse group representing many elite and non-elite undergrad institutions, but the individual likelihood of success from those schools is dramatically different. Williams may have 10 kids apply to HBS…Michigan might have 50? When each school has 5 admitted, the likelihood that a student from Williams gets into Harvard is 5X vs Michigan.
That example is a complete fabrication, but the probabilities for grad school acceptances at elite schools are (in my estimation) much higher than larger institutions.