exactly. the house insurance has to cover personal injury on the property to protect it from law suits. this will cover accidents for your family too. most people dont read their policies and really have no idea what is covered or not.
same with medical coverage with your car insurance. most of them cover so many people for so much per person in the event of injury in an accident. the minimums for this are usually set by state law. even if you dont cover your car itself(called full coverage), you have to have liability and medical.
its a racket. most people just sign the papers and pay the bills and never know what they are buying with their money. the insurance companies like it that way - fewer claims to pay!