It really depends on what sort of behavior the student is engaging in. Students should be allowed some form of privacy. There are exceptions, however. If a student is posting questionable photos of things they are doing in their dorm rooms, that is one thing. Plus, any propensity towards violence should be investigated.
If a student has committed a crime, it is the job of law enforcement to punish this person, not their university. Educational institutions have no jurisdiction to punish students for questionable behavior online. As long as the behavior conducted online is protected by the first amendment, no crime has ocurred.