It also helps the audience in case they missed the question. If the interviewer asks a negative question, rephrase it positively rather than repeat it. If the question contains incorrect information, correct it. Don't let the reporter move on until you are confident the point has been cleared. A TV reporter is doing an interview whether the camera is on or not.
Any statement made in the presence of the reporter or photographer is fair game.
You are never off the record simply because the camera is off. Plan to say Caltech a few times during a broadcast interview. The producer and reporter might forget to mention your affiliation. Then you can go on to enlarge the point with background. This will lessen the chances of having your remarks edited out of context.