He sent a private message and Avenatti published it. That's his fig leaf.
What I wonder is whether his email identified his affiliation with the school. That would have been a serious mistake. If Avenatti tracked him down and outed him, his fig leaf just got a lot bigger.
Apparently is Twitter profile identified where he worked.
Word to the wise. If you want to engage in war with leftists on Twitter, make sure you have a profile slicked of all ties to your real life. Sure, they can still figure out who you are if they want to but at least you'll have a fighting chance.