Graduate/professional programs are a different world than Ivy/Law school admissions in terms of what matters. "Prestige" is highly field-specific. In spite of what Harvard might like to think, they don't turn out the "best" graduates in every field that they offer a diploma in.
I think my law school roomate got about zero value out of his random Harvard masters degree in some environmental/policy thingy.
Each career track/field has their own entry points and value for degrees.
As an example, one of my other law school roommates had a brother who went to Stanford undergrad. His parents were quite willing to pay for him to go to med school. However, they weren't willing to pay for a more "highly ranked" private med school when they knew that the local state med school would do just fine. They were well aware of the difference in prestige in terms of ability to succeed in a profession with respect to med school and law school. They were fine paying for Stanford undergrad.
They had plenty of money, but they weren't interested in wasting it, so it was a cost-benefit analysis.
