While so much of the cost is the care that the organizations provide and what they choose to charge there is some truth to what you are saying.
Had to get an MRI and the lab corporation that performed the MRIs said that it would be ~$850 if billed through insurance. This included the total cost minus what was covered by insurance so the initial cost of the procedure was in the ~$1200 range. BUT, then they said if we just paid them directly and they didn't have to bill through insurance it would only be $650. So our insurance didn't even cover the absolutely ridiculous amount of overhead that was added just to deal with our insurance provider.
Had to get an MRI and the lab corporation that performed the MRIs said that it would be ~$850 if billed through insurance. This included the total cost minus what was covered by insurance so the initial cost of the procedure was in the ~$1200 range. BUT, then they said if we just paid them directly and they didn't have to bill through insurance it would only be $650. So our insurance didn't even cover the absolutely ridiculous amount of overhead that was added just to deal with our insurance provider.