I've had pretty much the same story, althouygh in my case it was a man claiming to live next door. "Oh, you must be the new neighbour, Kiki". "Err... yes", says he, thinking how lucky it is that I've heard of a new neighbour but haven't met them. "Be gone, you scoundrel", says I, "because I know Kiki and SHE doesn't look anything like you..."
Though I must admit it wasn't 5:34am so I was wide awake and alert when it happened... By the by, doesn't anyone know their neighbours anymore?