Loner streak
Someone who hates being alone doesn't have a loner/independent/freedom loving streak, it's either rejection by others that results in their being alone, or their peers aren't going to keep putting up with their bullshit (or both), depending on the person.
The girl wasnt really a rebellious, freedom loving, independent loner like she wanted people to think. People that actually knew her knew that she hated being alone and was needy of other people around her, though they were fine without her, but she wanted to fit in with her group like a chameleon/reptile by pretending to be fine without them around, so she assumed the freedom loving, independent, loner streak image (defense), since it had seemed believable enough when most people asked or investigated her true nature. In life, she actually had people who broke rules locked up or suspended, which was the opposite of rebellious, and was about as pro-authority/hierarchy as anybody could get. With the loner streak image, she could look like a friend to people on all sides to continue playing all sides.