BTW Pell grants have restrictions on school as well (many vocational institutions do not adhere to such restrictions, so they are not qualified to accept Pell grant money). The below are examples of such requirements:
Accreditation - Schools must be accredited by a recognized accrediting agency.
Compliance with Federal Guidelines - Schools must comply with federal regulations concerning how they manage and disburse student aid, including ensuring that funds are used properly and that students maintain satisfactory academic progress.
Non-discrimination - Schools must adhere to federal anti-discrimination laws <= this might be further strengthened to incorporate legacy admission as well.
Reporting Requirements - Schools must regularly report data to the Department of Education about their students, including Pell Grant recipients, and meet financial responsibility standards.
Misuse of Funds - Schools found to be misusing federal funds or engaging in fraudulent practices can lose eligibility to participate in federal student aid programs.
If a school does not adhere to such requirements, students cannot even find the school on FAFSA application to select. I remember one instance where school was delisted from FAFSA application (University of Phoenix I believe because they did not comply with federal regulations).