He should always be paranoid. ANY man should be paranoid.
Women are better cheaters than men. In my younger years (20s)...I was involved with women that were either married or with LTR boyfriends. Women that look normal and "decent" in front of their partners...but in the nightclubs were drunk and crazy.
If she was NOT into the alcohol thing, then I could see your point. But she drinks. She gets drunk. And there are lot of men out there. Make no mistake about that.
Furthermore...she goes TWICE a WEEK!!!!
He should NOT tell her what to do. He should understand that she wants to do that and will resent him if he prohibits her from doing that.
But he also has to understand that he is only 19 and he should seek what makes him happy. Way too young to be dealing with this crap, too be honest with you.