Well, sure they do. But the question is what holds them together beyond the physical plant and payment arrangements for students, faculty, and staff. Are they bound together by educational philosophy and practice that's consistent across departments and individual faculty? Writing in the NYTimes, Kevin Carey says that, no, they don't exit. It's a shell game:
This goes a long way toward explaining why colleges spend so much time and effort creating a sense of tribal solidarity among students and alumni. Think of the chant that Joe Paterno and students cried out together at the height of their university’s pedophilia scandal: “We are! Penn State!” The costumes, rituals and gladiatorial contests with rival colleges are all designed to portray the university as united and indivisible. Newer colleges that lack such deeply rooted identities spend millions of dollars on branding consultants in order to create them. […]People can learn a lot in college, and many do. But which college matters much less than everyone assumes. As Mr. Pascarella and Mr. Terenzini explain, the real differences exist at the departmental level, or within the classrooms of individual professors, who teach with a great deal of autonomy under the principles of academic freedom. The illusory university pretends that all professors are guided by a shared sense of educational excellence specific to their institution. In truth, as the former University of California president Clark Kerr observed long ago, professors are “a series of individual faculty entrepreneurs held together by a common grievance over parking.”The problem for students is that it is all but impossible to know ahead of time which part of the disunified university is which. Consumers of higher education have been taught that their main choice lies between whole institutions that are qualitatively different from one another. Because this is wrong, the higher education market often fails, which is probably one reason that a third of students who enroll in four-year colleges transfer or drop out within three years.