I honestly have no idea what they're implying by the words "middle school" in this context.
I've heard the suggestion before that even in this country there are some three-school systems, but I'd never even heard of a three-school system until I was almost done with school entirely. We just had Primary School and Secondary School (i.e. Comprehensive School / High School). End of. I used to think it very odd that Americans had three, then I learnt Japan had three as well. Then somewhere along the line I got to hearing that it isn't unheard of in Britain. I've never actually seen it though.
Plus she is 15, nearly 16, and apparently that puts her just at the start of this "middle school"? How? Were it a normal British school system as I know it, that would put her around Year 11, I think.
I'm guessing it might be that they've merged together some sort of University and School system in this, which would count the Uni as the 3rd school. But that might be a stretch.