That means most schools pretty much have to adopt some kind of cloud based solution that allows network administration of all of the computers used by the students.
I don't know why Google's privacy policy isn't worded the way you would like, but one reason is probably that wording it in a very strict way prevents any kind of evolution of the software product. For example, if you say "we don't track activities of school students", what does that mean? Does it mean the classroom software can't notify teachers about student behavior problems? Can't show a statistical dashboard for them? That 'auto-suggest' and Google Now-style assistive features (e.g. "You have an upcoming assignment due, and estimates based on your past speed of doing them says you should start today.") can't be offered?