IANAL, but this is from the linked bill text:

> (2) “Independent institution of higher education” means a nonpublic higher education institution that grants undergraduate degrees, graduate degrees, or both, that is formed as a nonprofit corporation in this state, that is accredited by an agency recognized by the United States Department of Education, and that receives, or benefits from, state-funded student financial assistance or that enrolls students who receive state-funded student financial assistance.

https://leginfo.legislature.ca.gov/faces/billCompareClient.x...

Seems like an institution is free to be fully private (not take state funded financial aid) and do whatever they want.