From Romenesko:

"Fresh Air" host Terry Gross tells Columbia students: "Before we start taping, I tell my guests that if they figure out what they really mean to say in the middle of saying it -- that is, if they figure out a clearer, more concise way of making their point -- they can go back to an earlier part of the answer and do it over. This sounds like sacrilege, I know -- it risks giving an interviewee an opportunity not only to rephrase a point but possibly retract it. But I really do want to give my guests a chance to say what they have to say as clearly as possible. Sometimes Im even the one suggesting they try it again."

From my experience doing radio interviews for Um... last year, this never happens. If anyone gets to stop and start over, it's the host, not the guest. I tried to stop and start over with one show -- it was my first interview, I'd quickly learn doing a number of live shows that forward, forward, forward was the direction of choice, which was something of a challenge for me, as I'm a reviser and a planner, an ummer, not a sentence restarter -- and my assuming the host's prerogative didn't go over well. That, and it made for some hell for the guy who edited it.