That's probably part of it, but I think the root is that a college campus is designed for people to use it without cars. Food, stores, classrooms, places to sit and meet are all built in and connected via walkways. Cars become unnecessary once you get to campus
A college campus is its own sustainable self-perpetuating institution. Or at least has been for much of the past century in the US (and elsewhere) as 1) an increasingly technological world has increased the need for an educated populace and 2) funding for college education has been readily available.
You've also got a town structure which is based on a single identifiable economic centre, which doesn't generally rely on heavy industry or ag within that centre (information, knowledge, and people, as well as the support strucutures for them), and so your principle transportation problem is how to move a fair-to-middlin' mostly younger and healthier population around. Bikes and walking fit this mode well, the small population of elderly and disabled can be accomodated as edge cases.
Keep in mind that in many small college towns, there's still a sizable commuter population. Some of that are students priced out of local housing, though the workforce is a much larger component, and may have commute patterns comparable to that of a large city (driving in from an hour or more away). The centralised nature of employment makes even rural mass transit or commuter shuttles viable.
There are still plenty of cars around college campuses and parking is a perpetual issue. Certainly faculty and staff (and some students) drive in and park daily. And even a town built around a relatively small college like Hanover NH still has a population of over 10K people.
ADDED: But, as others have noted, once you drive somewhere at least relatively close to where you're going, at least small to mid-sized campuses and associated towns are generally designed to let you walk to stores/restaurants/etc. fairly easily.
That's likely a consideration, as are the concentrated sources of value that are classrooms and labs with face-to-face instruction, as well as interaction (both social and educational) among students. Online education is reducing the edge of the former, though the latter is still hard to replicate outside of a college town.