Information provided on the FAFSA cannot be released to anyone who does not have an educational need to know. For example, a development staff might want to use it to target rich parents … but they cannot do so, as the school is required by law (enforced by very high monetary penalties) to restrict this information to only those who need it for educational purposes. Aggregate information can be released if it wouldn’t allow individual identification of a student, but individual information is very carefully protected.
And information about immigration status cannot be provided to anyone, including government agencies other than Federal Student Aid, which can only use it for processing purposes.