They key point was you were "impeding traffic".
I doubt they cared who towed it. They just wanted it off as quickly as possible. They probably do have agreements on who to call but if you got another tow company out first, I can't see them telling you to wait for the official one.
As a traffic engineer, you would be amazed how much reduction in capacity and delays can be caused by a simple broken down vehicle. Even if you are fully on the shoulder, it can cut capacity by 10-15%. During rush hour this can push a freeway into jam conditions and literally cost tens of thousands of dollar in driver lost time and extra fuel consumption plus ancillary crashes.
You don't have the right to continue to impede traffic because you are trying to save $20 on a tow.