I was listening to an interview with Italian historian Alessandro Portelli, and he was talking about oral history interviews. He said, "Think of the interview as opening a space."
That is exactly what it boils down to. The memorable story you get at an interview is rarely the one you went in expecting. Of course, if you have a list of prepared questions and don't venture beyond them, you'll never hear that story.
Just this past week I was interviewing someone and although he was a bit reticent at first, as we talked more he opened up and told me some wonderful stories. The space was open, and he walked into it.