Postsecondary institutions are accredited by the federal government?

No, postsecondary institutions in the United States are not accredited by the federal government. Accreditation is a process carried out by private, non-governmental agencies recognized by the U.S. Department of Education or the Council for Higher Education Accreditation (CHEA). The federal government recognizes these accrediting agencies, but doesn't directly accredit institutions itself.