Insurance in the USA

I am going to the USA to visit my brother and his family. I have hired a car for 4 days in order to visit Washington DC, but for the time we are staying with my brother he says I can drive one of his cars.
He says his cars are insured for any driver he gives permission to drive them. He says insurance is not a problem as his policy will pay out if his car is damaged. However, what about liability insurance? I assume his insurance would not protect me from being sued if I am responsible for an accident. How can I get insurance to cover me for such an event? My own car insurance company (Direct Line) don't offer it.
It's not a problem when hiring a car as insurance is sorted at the time of hire. Anyone know how to proceed if you need insurance to drive a relative's car?