Ironically, the Newman Society has put that idea in reverse, bemoaning Notre Dame, Boston College, Georgetown as minimally Catholic and praising Franciscan of Steubenville, Ave Maria, and Wyoming Catholic as model universities. 

Each time I say Notre Dame, BC, Georgetown, Fordham, and some others are among the few who can make this claim: Great Catholic University and Catholic Great University, I ask the Newman Society to tell me "their" universities that can make that claim--and I never get an answer.