At the campus envisions a university campus as a single point, like an arrow on a Google map showing a destination. On the campus locates something on a two-dimensional space which contains buildings and other facilities and can be peopled by student, faculty, or squirrels. On campus and off campus, without the definite article, refer to things or activities inside or outside the limits of that space.
Because he had never ventured out this way before, having generally confined himself to the city proper, he arrived at the campus three hours before the game was scheduled to start ...
We had travelled by train and turned up at the campus to meet Professor Andrew and other staff members.
What’s topical in these two sentences is travel and arrival at a destination, not the campus as area/environment. In the following sentence, however, a new professor arrives:
Before he arrived on the campus of Northwestern University in 1939, G. Donald Hudson had collected several years of experience in applied geography, teaching, and educational administration.
Since Dr. Hudson will be teaching at Northwestern and spending a great deal of time there, campus as environment is topical and his travel there is not. One can sense the same distinction in these two examples:
Although some people on the campus said the professor had been joking, the student clearly felt he faced a hostile environment.
Some people at the campus wanted to initiate professional degree supplemental tuition for this program.
People on campus suggests the writer had interviewed them on the spot, and environment guarantees thinking of the campus as a public space in which people are expressing an opinion. In the second example, only the opinion is topical, expressed by faculty or administrators from the university.
A university with more than one campus will distinguish them as single-point locations, with an implicit or explicit contrast with other points, like these two Texas universities:
Third- and fourth-year medical students currently train at the El Paso campus, along with residents in eight accredited programs.
There was a specific decision that all members of the original student affairs staff should have experience working on the main campus for many years prior to their assuming a role at the campus in Qatar.
The main campus of Texas Tech is in Lubbock, but medical students can also train at a different location, regarded as as single point. In the second example, employees work on the main campus of Texas A&M in College Station for many years like Dr. Hudson, but then assume a role at the campus in the Persian Gulf state of Qatar.
As this last example suggests, a person can work on or at the campus, so, for instance, in these two examples from the same article about a research center in North Carolina:
Dayvault, 27, works at the campus. From the balcony outside his second-story office at the UNC Nutrition Research Institute, Dayvault can look out over his ancestors’ land, which went from cornfield to Town Lake to Core Lab.
About 600 people now work on the campus, including the employees at the new Cabarrus Health Alliance across Dale Earnhardt Boulevard.
Were the two prepositions reversed, there would be no change in meaning, only in the way campus is envisioned: point or space. The same is the case when talking about these two museums:
These archaeological discoveries were deposited in 'the Eretz Israel Museum' at the campus of Tel Aviv University, a historical and archaeological museum in the Ramat Aviv neighbourhood of Tel Aviv.
We went to the Arizona State Museum on the campus of the University of Arizona, Tucson. The museum was focused on Native American history, pottery and baskets.
On campus and off campus parse as compound adjectives or adverbs rather than prepositional phrases: a dry cleaner just off campus, off-campus housing, an on-campus fast food franchise. Here, the boundaries of campus as space are important, not the space itself:
When a student works on campus, there are only so many job opportunities.
Other factors include the schools services to help students move off campus and how easy it is to secure housing.