An individual cannot acquire knowledge by cheating on an exam, or plagiarizing in an essay, thus proving the need for these simple virtues. Since the code of conduct already covers universal morals, and students across the globe are aware that dishonesty in their work is unacceptable, there is no need for further moral instruction in the university.
On the other hand, it would be appropriate for an unaffiliated university to offer a course, perhaps under one of the general education categories, on the moral beliefs of various cultures. This hypothetical course would not emphasize, or encourage any one set of morals in particular, but would cover a wide range of cultures and religions. Since the students would register for the specific class and are only being exposed to various moral beliefs, their ethnic background would not be a controversial matter. Instead, the morals would be approached and discussed with an open mind making the student culturally aware of different moral beliefs. .
A different situation occurs when students are entering a university that is affiliated with a specific church. Students can already expect their education to contain, and even encourage, deeper concepts of morality based on that particular religion. For example, it would not seem odd for a student enrolled in a Catholic school to take a class on the importance of an ethical life from the perspective of the Catholic Church. Considering that these colleges are smaller, contain a student body of the same religion, and advertise the institution as one of religious faith, they may be obligated to provide their students with an education based on religious principles that suit their beliefs. This is more than basic universal morals and therefore can be taught to the specific group that is interested.
Although the unaffiliated university should not teach morality directly, it can be aiding the student in becoming a moral person by requiring discourse and actions from the student based upon their beliefs.