Actually it goes beyond just setting the rates. The state sets the rules. The state can "fire" drivers. Managing transportation is core to what government does. According to the ABC criteria, they should qualify as state employees with all the ensuring benefits and it would be hilarious if all taxi drivers in California sued the state to become state employees just like bus drivers and train operators.
I don't know about other states but in mine there is no medallion. You can start a T&L company today if you wanted to. You only need to read up on the state and local certifications, rates, livery, and vehicle requirements. Most of the taxi drivers I've used are actually employees of a T&L company.
By that logic all taxi drivers are employees of the cities of their medallion, because cities set the taxi driver rates.