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I always did, and since I learned to write at a young age and can draw pretty well I was very resistant to anyone telling me to change it. I only taught myself to use a tripod grasp when I became an OT and wanted to be able to demonstrate tripod grasp for others.
When you hold a pencil the way we do, you get more stability and feedback from the pencil because it rests on your largest thumb joint. You might lose fine manual control in that position if you hold it stiffly, but I don't and I'll bet she doesn't either. The only drawback is fatigue if I write a lot - we're generally using more pressure than most people.
It points to someone who likes a lot of feedback from her body. I was always active in dance, gymnastics, and now martial arts. That doesn't mean I was naturally coordinated, but I just loved using my body and still do.

When I saw that she was comfortable with that grip I was nervous it would affect her writing but she writes just as normal as anyone else.

Okay...you may have helped her with something. When she writes for awhile
(particularly cursive writing) she starts complaining how tired she is and that she can’t write any more. I always think she’s just trying to get out of her writing lesson (she’s not fond of cursive writing right now). She’ll lay both arms out on the table and rest her head and tells me she needs to take a break. This explains why she seems exhausted when doing her writing lessons.

Wow, I’m so glad you came to visit and shared this with me. Thank you! I will be more sensitive to her needing breaks in between :)