We see things elsewhere in the Darkfriend world where beggars can give orders to nobles, so who is to say that someone in a Daigian-like position might not rise to the Supreme Council. How influential was Alviarin, after all, in the White Tower? It is far more likely that her rise as Keeper owed more to her leading the Supreme Council for over a decade than her rise to the Council resulting from some unsubstantiated & speculative status she may have held in the Tower.