Most
scholarships through a school are either Merit-based, meaning they require a high GPA or other academic qualifications, or need-based which go to the most needy students. It sounds like your school uses a student's FAFSA information to determine eligibility for their private scholarships. It does seem fishy that they promote the scholarship as not need-based and still base the decision on finances, however, the means through which a school determines scholarship recipients is completely up to them.
If you are still in need of aid, you can try looking for other applicable scholarships through
StudentScholarshipSearch.com.
Good luck!