Both institutions work in tandem[0] with one another to establish pricing guidelines. That's why your hospital-purchased ibuprofen is $10 per pill instead of $6 per bottle. The insurer and hospital "work out" a price that let's them achieve the profit needed to pay their administrative costs, plus margin.
In the USA(this is all from a US citizen's perspective), there are regulations that limit what percentage(15% in my state) of an insurer's income can be profit vs administrative cost. This means that a higher hospital price results in a higher profit for the insurance provider. This provides both parties an opportunity to set prices for an optimal profit. With government-mandated health insurance participation, the pool of people paying into this system has increased.
It is what is. Tell your elected official if you think it would help.
0: Anthem, Blue Cross, and UHC executives sit on the Baptist Health(hospital chain) board of directors, and vice versa.