"Now, unless "the provision of services and employment" mentioned under Titles VI and VIII reach college admission, than none of the above extend Constitutional Law principles regulating state action to non-state actors with regard to race and college admission, except as regards students in health personnel college programs".
As to the last point, I seem to recall a Mississippi case involving a nursing school that was likely the precedent for that law.
"(c) "Public school" means any elementary or secondary educational institution, and "public college" means any institution of higher education or any technical or vocational school above the secondary school level, provided that such public school or public college is operated by a State, subdivision of a State, or governmental agency within a State, or operated wholly or predominantly from or through the use of governmental funds or property, or funds or property derived from a governmental source. "
Note the requirement of "predominately" re funding.