Automobile insurance covers the owner of the car, the driver of the car, and/or an insured driving a temporary vehicle. If the company owns the vehicle, the company needs to provide liability coverage for its risk of operating the vehicle on the road.
As a driver, you need liability insurance even if you don't own a car. Drivers are held responsible regardless of ownership. Entrepreneurs who own a company car and a personal car need both policies.
If you drive your car for business, the company still needs liability insurance to protect against the risk of operating a vehicle on a public road. Tangential issues include: