Have you considered the real possibility that the reason she is able to be so independent and self-sufficient is because she feels very secure in her relationship with you?
I have a friend who was exceptionally independent as a teen, and looking back, I think a very large part of it is because of her relationship with her mom. They were not the chummy, demonstratively lovey kind of mother-daughter pairing. They may have even seemed somewhat aloof from the outside. But from the inside, they had a level of respect for one another (both quirky, and wholly accepting of that in one another--at an age where most kids found their "regular" parents unforgivably embarrassing). I really think that freed my friend from a lot of the insecurity that kids that age feel. It made her bold and fearless. Not in the reckless kind of way. But in the independent and self-sufficient kind of way.
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Mom to 2 exceptional atypical kids
Long BAP lineage