I actually asked this question when attending a taping in 2000 and this is roughly what Johnny Gilbert told us:
At the table you occasionally catch a glimpse of on air are sitting the producers. If there is a question about whether a response is accurate or not, they make the decision most of the time.
If there is a further question as to whether a response is valid or not, all of the writers of that days material are sitting off site and watching the proceedings on monitors. Taping is stopped and the writer responsible for the "answer" in question will provide the producers with the source for his or her material. They will also check to see if the players response was valid or not which is why you will once in a great while see them come back from a break and say "upon further reflection it was determined your answer was acceptable..."