This isn't the only thing driving that effect. In any situation, a price tag can be higher when those receiving the service don't feel it in the wallet immediately, whether for reasons of insurance or even loans (homes, tuition, etc.) and those facilitating (insurers, lenders) would surely be incentivised to do whatever they can to make using their services the best way to get a fair price. Look at rental car rates where a retail walk-up customer pays double or triple what insurance pays -- for the same exact car.
This is also true. "Your health insurance benefits for optical have reset, would you like to come in for new glasses?" "Well sure, my current ones are fine if the new pair is gonna be free..."
