Fair enough, but that's kind of hard to show in an interview. My typical experience is that the first couple of months on a job, I'm soaking the whole place up (i.e., figuring out their unique accumulated horrors), and my bosses typically have no idea what I'm doing (and are thinking they made a mistake hiring me).
Then suddenly (to them) I start becoming really productive, and in short order they realize I'm the guy who can solve the problems no one else can. Once had a boss cry when I turned in my notice.
But how do you sell that?