Some members believed in protecting the Traveler, while others were concerned with controlling him and possibly defending Earth against him. Apparently Dr. Swann's point of view was cautious but open-minded: he seemed to believe that the messages pointed to a threat or invasion, but upon actually meeting the Traveler himself, he decided to protect him and his secret. He even founded companies such as in order to help The Traveler learn more about himself and the planet around him.
By the time Dr. Swann translated the Kryptonian message, it can be presumed that Veritas had disbanded, because Dr. Swann claimed to that he did not reveal the message to any of the other members. However, Lionel eventually learned the Traveler's name was "Kal-El" and that Kal-El, the Traveler, and Clark were one and the same.
Proust is better at writing about jealousy than any other modern author. He describes Swann as becoming jealous of an earlier version of himself, the man whom she first declared her love for, the man he used to be before the disease took hold and the peverse pendulum of power swung to the other side.