I think a lot of people only look at this situation from a football recruiting standpoint. It's not a football thing, it's a school thing.
CDH, as a school, is always going to argue that a private school education is better than a public. They are a private school, it's not free to go there, and they are in the business of telling people that they should pay for something that would be free, because it's better than the free thing. So yes, as an institution, they are going to be bias towards private schooling. It's evident in the entire school.
I knew way more people that attended private (usually Catholic) schools than people who attended public schools. St. Thomas and St. Johns are full of Cretin alumni, Cretin kids are choosing those schools over St. Clouds and Winonas. It's often not a money thing, I knew a lot of kids at CDH who didn't grow up with money.
As a Cretin alum, I think it's overblown. I don't think my high school education was any better than my public school counterparts, but it's the perception in every private school or else they wouldn't exist.
I know nothing about Jashon Cornell's life and I'm not attempting to assume he is in this camp, but that private school bias is especially true for the kids from rougher neighborhoods. These kids, if not for CDH, would have ended up at inner city schools, where the achievement is less than the burbs or Cretin. So that bias gets engrained intheir family. They see their kid achieve a ton at Cretin and their neighbors' kids having trouble at North, it cements that bias.
It's a private school thing, not a football program thing. Ray Hitchcock is about the biggest Gopher fan in the world.