All the part of the law they're referencing really does is attempt to make paperwork easier. Race is always either identified by student or parent. In older grades, typically by the student. This allows the school to bypass parents in certain situations. This is because there are cases where parents have conflicting views on a child's race (there are situations where one parent will insist a student is black, and another insists they are not), situations where parents are nigh impossible to get a hold of, situations where a parent refuses to answer questions of race, and so on. And of course, there is the situation that you have kids who are old enough to self identify race, (so far from my experience, about 100% of students identify race as you would expect) and you have no need to involve parents. Of course, the law preserves the school's ability to consult parents, and use them as the determining factor.
Of course, all this does is dictate what goes into a field in a computer system. Which... I guess is a big deal to some people?