FAFSA is only binding for Department of Education money, which is approximately nothing for a middle-class student at a top-tier school. Most of the reduction off the $60k sticker price comes from university grants, which universities can apportion as they see fit. Many use a combination of the FAFSA, the CSS PROFILE (which is more resistant to asset-hiding), and sometimes proprietary forms.
With CSS PROFILE it sounds like it's just that some schools ask for parents information anyway:
When can a student fill out the PROFILE as an
independent? A student is considered independent,
for financial aid consideration, if he or she is
or has at least one of the following: is at least
24 years old as of Jan. 1 of the academic year,
is married, is a graduate or professional student,
has a legal dependent other than a spouse, is a
veteran of the U.S. Armed Forces, or is an orphan
or ward of the court (or was a ward of the court
until age 18). If not, the student is considered
dependent. A parent refusing to provide support
for his or her child’s education is not sufficient
for the child to be declared independent.
Financial aid eligibility is, in part, determined
by a student’s dependency status. Independent
students are treated differently from students
who are dependent on their parents. However, some
schools and programs require parental information
on the PROFILE even if the student is considered
independent based on the criteria above.