I think most regulated taxi companies are likely in the same insurance avoidance plan as Uber. A medallion owner can "rent" the cab to a driver as an independent contractor. The taxi company provides a way to offer fares to drivers, but they will not place an obligation to the driver. The driver is free to pick up fares on their own. This places the company in a position to argue that it is not responsible for the actions of the driver, as the driver is not an employee and not acting under specific direction of the taxi company.
forcing drivers to provide insurance is easy, and even easier for Uber and Lyft as they dont own the car/medallion and are not leasing/renting/checking it out to the driver. Many of these drivers know that they are uninsured while using their car in a commercial activity, which scares the hell out of me.