The university will only catch you if you're uploading content using a file sharing method. The reason for this is if you own a copy of a movie or TV show, by law, you are allowed to create backups of that movie/TV show, so you can legally download it.
If you use a torrent client like Transmission, you can set the upload rate to 0, and it won't upload at all.
Like I said, as long as you're not uploading, they can't prove that you're doing anything illegal. There is no way for them to distinguish someone making backups of their purchased music collection, and someone pirating music. (Same goes for movies, software, and the likes)
my friend got her internet suspended and had to have a meeting with the housing ppl because she downloaded 4 songs from the internet.
the problem was, she didn't download them and she was mistakenly identified as downloading these songs (they also knew what songs she "supposedly" downloaded)
She probably was uploading by accident (that's the default setting for most clients, and if you don't change it-- you're uploading without knowing it).