She's wrong. You're right. Full stop.
HOWEVER, one other piece of information that may be helpful (as in if she throws some variation of this at you and you can say "yes but that's a special case..."). I did take college classes in 11th and 12th grade, at no cost to me. For example, when I was in 12th grade and hadn't yet graduated, instead of taking a science class at my high school, I took an astronomy class at the University of Minnesota, and that was paid for. I don't remember the name of the program and don't know how widespread it is.
There are also AP classes, which are a similar concept but work differently in terms of where you take the class. (It is taken by high school students at their school; the class itself is merely at a higher level than standard high school classes.) "AP" stands for "Advanced Placement." You often (maybe always?) get university credit if you pass an exam at the end of the class. So I took, while still in high school, an AP English class that allowed me to skip an introductory university freshman English class. I had that credit on my transcript already, before I started university.
AP classes are usually offered in 11th and 12th grade, and if your opponent has any meat to her argument, that's probably it.
More info:
http://www.collegeboard.com/student/testing/ap/about.html