I think you need to call the insurance provider. It may be that if the primary doc refers the child that they will cover it. It is medical care and I don't see how any insurance company can not cover it. That's like saying they cover all health problems but have selected to not cover any health issue that is related to the heart.
I think that if a primary care doc says they need to see someone they have to follow through. It's a medical need. Maybe not therapy or something but for medication I don't think they could do that.
Look in your area for a free or low income mental health clinic. You will need to see a psychologist that is qualified to evaluate for a diagnosis to receive medication from a psychiatrist. They just won't see anyone who wants to put their kids on meds. They have to have a doc's evaluation that is qualified to make that determination.
If you have a teaching medical college nearby call them and find out if they have children's services. They should have a pediatric mental health department. That department could do evaluations and also have a psychiatrist on staff.
We took my grandson to a psychologist for evaluations this past spring then also went to OU Health Science Center this summer to the Pediatric mental health department. He did evaluations and is now on meds.
We didn't have to pay anything for any of his care. The state medical card covered it. If you do start making more money then you just pay a portion that is based on income in a lot of places. You can always find out through the insurance provider when you call them. It might be that he just didn't sign up for the mental health part when he did his plan this year.