I think the dude should have been firm and confronted the girl. He has an idea that she's ...

I think the dude should have been firm and confronted the girl. He has an idea that she's a liar and that she likes him but he didn't want to deal with it or confront her so he just let her keep the sweater. Avoiding toxic people by letting them have their way further enables toxic behaviors. It's going to end up exploding in their face if she ends up catching them together. She'll feel betrayed and led on even though that might not be his intentions. Deal with the rotten mean girl now rather than later