I was at this stage once, moving out of the fundamentalist religion mindset into a mindset of spirituality (for lack of a better term).
She is struggling with losing her label as Christian, because it is most likely how she has defined herself for years. Also, she most likely sees the fallacies in organized religion, so instead of rationalizing them, she is branching off to make her own beliefs that she learns through personal experience, knowledge, and growth.
She uses "Jesus" because she feels comfortable with this anthropomorphication of aspects of God. She most likely sees the figure of Jesus as a role model, a standard for her to constantly strive for. She is not ready to let go of the concrete perception of Jesus presented by the church because that would cause her to break from any kind of spirituality, and imo that would not benefit her.
This is speculation, but perhaps if you want to know more from this person, you could talk to her more and try to find out what she thinks about life, the universe, and everything.
I would suggest not to judge, but seek to understand, even if you still think she's nuts
Edit: I just read your post about her "newfound" religion. In that case, she probably is grasping the positive message hidden in the craphole of organized Christianity, so she doesn't want to associate with the church, but likes the spiritual message she has ascertained from it.
Again, speculation. Go talk to her
