That’s exactly the quote that struck me also.
JPII issued the following regarding Catholic universities.
vatican.va/holy_father/john_paul_ii/apost_constitutions/documents/hf_jp-ii_apc_15081990_ex-corde-ecclesiae_en.html
From the encyclical, where a Catholic university would fail at being Catholic
§ 3. In ways appropriate to the different academic disciplines, all Catholic teachers are to be faithful to, and all other teachers are to respect, Catholic doctrine and morals in their research and teaching. In particular, Catholic theologians, aware that they fulfil a mandate received from the Church, are to be faithful to the Magisterium of the Church as the authentic interpreter of Sacred Scripture and Sacred Tradition(50).
§ 4. Those university teachers and administrators who belong to other Churches, ecclesial communities, or religions, as well as those who profess no religious belief, and also all students, are to recognize and respect the distinctive Catholic identity of the University. In order not to endanger the Catholic identity of the University or Institute of Higher Studies, the number of non-Catholic teachers should not be allowed to constitute a majority within the Institution, which is and must remain Catholic.
§ 5. The education of students is to combine academic and professional development with formation in moral and religious principles and the social teachings of the Church**;** the programme of studies for each of the various professions is to include an appropriate ethical formation in that profession.Courses in Catholic doctrine are to be made available to all students(51).
Article 5.
The Catholic University within the Church
§ 1. Every Catholic University is to maintain communion with the universal Church and the Holy See; it is to be in close communion with the local Church and in particular with the diocesan Bishops of the region or nation in which it is located. In ways consistent with its nature as a University, a Catholic University will contribute to the Church’s work of evangelization.
§ 2. Each Bishop has a responsibility to promote the welfare of the Catholic Universities in his diocese and has the right and duty to watch over the preservation and strengthening of their Catholic character. If problems should arise conceming this Catholic character, the local Bishop is to take the initiatives necessary to resolve the matter, working with the competent university authorities in accordance with established procedures(52) and, if necessary, with the help of the Holy See.
§ 3. Periodically, each Catholic University, to which Artide 3, 1 and 2 refers, is to communicate relevant information about the University and its activities to the competent ecclesiastical Authority. Other Catholic Universities are to communicate this information to the Bishop of the diocese in which the principal seat of the Institution is located.