I think it's more likely a case of your professor being a bit off or outdated. While the school can set policy, a stubborn professor who doesn't like the tech can often set their own policies to skirt around it.
I got out of college 7 years ago and even then we were doing electronic assignments with NO paper turn ins whatsoever. We had tests where you came in and typed up your essay questions and then electronically submitted them to the instructor. Your grade then showed up in an automated system. At that point they were already requiring all incoming freshmen to have laptops for in-class use.
This in general I don't even see as a "green" issue. I'm biased as my degree is in Computer Science, but paper makes absolutely no sense to me in today's world. Why bother with a medium that takes up tons of space out in the real world and is incredibly time consuming to search.
I still have a saved electronic copy of every essay/paper I've written since high school. I've just copied the information from my documents folder from each system I bought each time. If I want to find an essay I wrote in high school about manifest destiny it's as simple as typing the following command:
grep -R "manifest destiny" *
Paper can't do that