I'm not a lawyer and I've heard of more ridiculous laws than that, so quite possibly, but even if that's the case, I wouldn't think it would cover billing x and collecting 0.1x when you realize someone can't pay x.
And even if I'm wrong about that, when lacking insurance I didn't encounter a medical provider, including big ones with big compliance offices, who wouldn't do it. But others' mileage may vary.
My understanding is that directly charging a different (higher) amount for insurance is considered to be fraud.