It's how IP addresses work when you stop thinking small.
The University closest to me has one external IP address. While each computer inside the network has a different IP address, the address Riot sees is the same for everyone there. 4,000 freshmen are admitted each year, many of which live in the on-campus housing that shares the same IP address. Everyone who moved into those dorms would be banned for a year, and no new players could start while living there.
Assuming a similar setup at other universities and you can easily have thousands IP Banned for the actions of a few dozen.