The Board shall retain the right of determining eligibility of lenders and holders of student loans to which payments may be made. An eligible lender or holder shall, in general, make or hold loans made to individuals for purposes of attending postsecondary institutions and shall not be any private individual. An eligible lender or holder may be, but is not limited to, a bank, savings and loan association, credit union, institution of higher education, licensed Texas hospital, licensed Texas long-term care facility, secondary market, governmental agency, pension fund, private foundation, or insurance company provided the loan conforms to the definition of an eligible student loan as provided in this subchapter.