I've been thinking about this myself. I'm trying to convince myself to go paperless, but I tend to crack and photocopy/physically distribute documents that I consider important, like the syllabus. Not that it makes a lot of difference--all the available evidence points to them losing/not reading the things I hand out in paper! (I also have problems with students not printing things out, so...) I think I do it because in the back of my mind I'm not sure if I'll get support from the higher-ups should a student ever want to challenge something by claiming that they weren't properly informed about it. The solidity of a paper syllabus is comforting in that regard.
See, I think using the university approved CMS or sending it to the students' university email would serve this purpose more thoroughly, as it can be solidly documented. I can't prove that I handed something out or said it in class, that the student was there when I did, etc. But I can say, "See, Dean, right there on the CMS that you keep telling us to use more!"