I didn't know that Tweeting was a protected right! Interestingly this only impacts players at private schools. I'm not sure what the rules are at Notre Dame to tell you the truth. But I can see why coaches would just as soon players not tweet things regarding the football program or whatever sport that they are playing. I could see the problems it might cause. http://www.usatoday.com/story/sports/ncaaf/2016/10/11/nlrb-gives-northwestern-football-players-right-to-tweet/91913588/?hootPostID=ac667fbad9653feedacfa2dff10e439f
It's basically a freedom of speech issue. The program can restrict player availability to media interviews, but you just can't restrict a kid on his own time using his own medium to reach out to the masses. The only upside is that no one has a corner on the market of kids that say stupid things.