"What is the responsibility of the university to maintain academic integrity? What else ought the university be responsible for in terms of academic integrity with faculty, students, staff, and administrators?"
The university seems to be pretty proactive about academic integrity, as it should be. Without academic integrity, there would probably be a greater number of people with graduate degrees because you could just cheat your way through various programs. Demonstrating and applying knowledge seem to be the basis for any education, and to graduate education is usually the added component of building or creating knowledge by performing research. When someone else has gone to so much hard work to create a research question, find appropriate/applicable methods and methodology, and then conduct and analyze that research, it's just plain rude and crappy as a human being to represent that work as your own. For that reason, I think the university should do everything it can to avoid situations like that from happening, up to and including expulsion, as the most extreme case of the Honor Code calls for.
In my field, plagiarism and cheating are hard to pull off because we do so much writing in which you are expected to make an original argument and/or perform research that you then present in writing. At the graduate level, our professors are so familiar with so many scholars in our field that I think you'd probably look like an idiot if you tried to pass someone else's work off as your own. Many of the professors in our department are on the editorial boards or the peer review staff of national journals, and because they read so many seminar papers, they can usually spot graduate submissions easily. I can't imagine what the consequence would be of submitting plagiarized or ethically sloppy work to an academic journal. You would surely be talked about, your work would be rejected, and you might not ever be taken seriously by that journal again. It's just too risky a gamble to take.