As I recall from my childhood it was commonly done in the 50's and 60's when someone was promoting a new movie or record release. Rather than trotting them across country to every radio and TV station they would pretape the celebrity answering a list of questions that the local personality would read and they would edit them into an "interview".
I read in a biography of Johnny Carson that when he was working in radio in Omaha just out of college, he would mess with those records kind of like was described above in Mad magazine. The example given was an "interview" with Peggy Lee where the DJ was supposed to ask, "How old were you when you first sang in front of people?" Johnny would instead ask, "You're really known for hitting the sauce. How old were you when you first started?", and follow with her pre-recorded answer, "When I was 5 or 6, I used to get up and do it." Premiere (and I'm sure lots of other prep services) offer "interviews" in this form. Depending on the interviewer or the producer, it can sound kind of real, or it can sound like "What was it like to do a love scene with Jessica Alba?...Play Cut 5."