I hadn't heard of the Scholarships for Disadvantaged Students, but your parent info is requested for the Health Professions Student LOAN and has nothing to do with your background.. only financial need. Again, the website doesn't give criteria, but your school could help.
http://bhpr.hrsa.gov/dsa/hpsl.htm
My college (UOP) gives the following directions for the FAFSA:
"Parent Information
To be considered for aid from the Health Professions Student Loan Program ( HPSL), fill out the purple section of the FAFSA and have one of your parents sign the form.
By regulation, parent information must be considered in evaluating eligibility for HPSL. Providing parent information on your FAFSA will allow us to determine whether a Health Professions Student Loan can be added to your financial aid package. (If you do not qualify for HPSL, we will disregard the parent data and your award will include only the funds you qualify for on the basis of student information, alone.)
HPSL awards cannot be disbursed until we have received and reviewed a complete, signed copy of the parent's 2007 U.S. income tax return."