From left, Ariadne Getty and her children, Nats and August, at Ariadne’s home in Beverly Hills, Calif.: A fabled family finds their showbiz portrayals “demonizing,” “disgusting” and unrepresentative of their super-L.G.B.T.Q. values. BEVERLY HILLS, Calif. — The Getty family is known for many things. A welcome to prying eyes is not one of them. Invite a reporter to run a tape recorder in the living room? Are you insane?