Espola is correct...state funding is not all from property taxes. Regardless, the State controls the purse strings.
Not sure I'm adding value here, but it depends on the district. Put simply, because public school funding is hardly simple (though LCAP/LCFF has simplified things quite a bit), it depends on the district. Some districts are "Basic Aid" and others are "Revenue Limit". Essentially LCFF says each district should have a certain amount of money per ADA. A basic aid district is one that doesn't need additional state funding because the local property taxes is enough to hit that number. On the flip-side revenue limit districts need additional funding from the state. Absolutely there are more revenue limit districts than basic aid districts.