“Nonpublic, nonsectarian agency” means a private, nonsectarian establishment or individual that provides related services necessary for an individual with exceptional needs to benefit educationally from the pupils’ educational program pursuant to an individualized education program and that is certified by the department. It does not include an organization or agency that operates as a public agency or offers public service, including, but not limited to, a state or local agency, an affiliate of a state or local agency, including a private, nonprofit corporation established or operated by a state or local agency, a public university or college, or a public hospital. The nonpublic, nonsectarian agency shall also meet standards as prescribed by the superintendent and board.