It's a vicious positive-feedback cycle where both parts are both cause and effect. You can also say that the insurance company also does that (fight to pay only a part) because the hospital bills too high for them. They're fighting to be billed fairly as the regular people are billed.

> if the hospital has evaluated that a CAT scan costs them $1250 to do

Remember that the fact that they can use insurance companies to drive up prices means they can also drive up their own costs.