A lot of schools operate on a shoe string, so it doesn't surprise me they would try to bill. I do think its legal, in US anyway, but there could be ways to fight if you cannot pay it. I'm not aware that such bills are a common practice because it seems to me they could trigger counter claims - for inadequate education, for example (in the US the law requires that schools provide an adequate education based on the unique needs of the child; if you feel forced to home school it would seem they haven't met that obligation).
I would probably start with an information seeking conversation, where you try to understand their policy without revealing your own strategy. Fighting already over burdened schools isn't something I generally believe in, BUT sometimes we have to in order to make things better for all special needs kids. So gather all the information you can and then decide what to do.
Do check with your private insurance, as well.
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Mom to an amazing young adult AS son, plus an also amazing non-AS daughter. Most likely part of the "Broader Autism Phenotype" (some traits).