When I was in high school in the 1960s I was in a wonderful math program, UICSM, which stands for the University of Illinois Committee on School Mathematics. It was a "new" math. I'm yet to meet someone who didn't go to my high school who ever heard of it. Anyway, one of the reasons it was wonderful was that it taught us to think, and we proved EVERYTHING. It was incredibly rigorous, and afterwards, some 30 years after taking my last high school math class, I was able to test into algebra 2. And when I was in that class, memories of what I'd learned all those years ago came bubbling up, and were very helpful.
Here's what's important, even though it's beyond the grade level you're dealing with. In the third year of UICSM, the last year I took it, we were well into calculus. I'd gotten A's in the geometry part, B's in the rest, but when we hit calculus, I could not understand it and just barely passed the final semester. So 30 plus years later I need to take math through college algebra. Ok. I take algebra 2, get a B, college algebra, get an A. I decided to take statistics because I thought it would be useful. Then, because I really was having a good time with math, I decided to take calculus. I was 47 years old. And I got it. I loved the class, what I was learning. My final grade was a B, mainly because I managed to make some dumb mistakes on the final, but I learned an A's worth. During the semester I kept on grabbing math teachers I knew at the community college I was attending and asking them how was it I was doing so well at my advanced age, when back when I was 16 I could not get it at all? To a person they said, "Oh, Poindexter. People don't understand that math is developmental." They'd go on to say that other than the real math prodigies, most high school students at 17 or 18 really aren't quite ready for calculus. Give them a year or two and they'd be fine. These teachers also felt that the local very good public schools were pushing a lot of kids a bit too fast and hard in the math, and needed to ease up.
I have shared that over and over with high school students and with their parents. They are often quite relieved to hear that. I saw this developmental thing with my younger son, who in the excellent private school he attended, was always at the upper edge of what he was ready for in math. I encouraged him not to take calculus, because he was struggling enough that it made no sense. He was very relieved, probably fearing that I would say to him, "Your older brother took calculus and did just fine so of course you will take it too."
So anyway, if the teacher thinks this girl is where she should be, please try to convince the parents to trust the teacher. It may be that in another year or two this girl will blossom in math and be able to get into the advanced program. If not, it's not the end of the world nor the end of her being able to do well in math in the future.
One frustrating problem with conventional schools is that of necessity they have to teach kids in groups, and everyone is expected to learn the same thing at the same time. I was up against that when my older son was having trouble learning to read, but was ahead of the other kids in math. Eventually everything settled, but it made me very understanding of why some people choose to home school.