Perhaps the simplest way to frame this question is to posit what kind of shit storm would happen if all of the details were made public? Would the uni defend the instructor’s use of torrents, which would be characterized unfavorably by the media? Or would the uni throw the instructor to the wolves?
That you are being so careful with all of the hypothetical suggests to me that you already suspect the university would not support this but want to do it anyway and are looking for some CYA reasons you can pull out in your defense if your actions come to light.
Some universities have a history of ripping DVDs themselves for playback. UCLA was sued over that, but the case failed due to lack of standing and was not decided on the merits. Universities have been playing at the edge of the law - it is just way more practical to serve the movies from DVD rips on a central server than to playback the physical media. Even so, I’m thinking that the universities want to decide that edge and not leave it up to their instructors, and that the unis and really don’t want to get noticed or associated with torrents.
Also, torrents might seem anonymous because faceless internet, but, in fact, they are about as public as you can get. If you download a torrent, your IP address is public - because that’s how everyone knows where to send the bits, and the lawsuits.
If you are not familiar with the ins and outs of torrents and you are a college instructor my suggestion would be: run away.
Ask other instructors how they get playback. You’d be better off ripping the DVD you own for classroom playback than torrenting it. It’s more in line with what some universities IT systems do. Much more justifiable if you are called on it.