I wanted to get an umbrella policy years ago, but ran into a complication. My Dad had bought a car, and put my name on the title, thinking it would make it easier to transfer to me when he passed away. I remember that being a sticking point...the insurance company was worried that, because my name was on Dad's car, it could theoretically get me into some trouble if he did something lawsuit-worthy with that car.
At first, they said they could just put it into the policy that they wouldn't cover anything resulting from that, but then, they simply refused. Well, Dad has passed away now. But, only problem is, I did it again. In 2012, I bought a new truck, and my uncle let me use his old one as a trade in. So, I put his name on the title, so he'd have my new truck if I died, with a minimum of fuss. At the time, Dad was still alive, so I wasn't thinking about umbrella policies.