We have a similar concept in Denmark, but here they are called "private schools", some of them are also called "Friskole", which can be translated the same way as the headline - the meaning is however that their metodes are "free" of the municipality decisions about education, not that they are free of payment, quite the opposite, they often require additional payment.
They get the same funding for each student as the public schools, if and only if, they meet certain requirements, basically the same law as public schools are required to meet. And specifically, they must be a "self owned" institution and all funding can only be used for the school and education. They are free to require the aforementioned additional payment, but they cannot be profit generating if they want funding from the government.