This is not the most authoritative proof, but from Georgette Heyer's Regency novels, I got the impression that marriages and weddings were hardly considered official until they had been published in the "Morning Post", a newspaper apparently favoured by the upper classes. Now, I don't know if this was only true of the aristocracy, or if the gentry did the same, but I do get the impression that JA's world was smaller than ours, and that the choice of "correct" newspapers was smaller as well. I suspect that if Anne read the "right" newspaper regularly, including the weddings page, she might have a good chance of discovering whether Captain Wentworth had married or not. Remember the importance in P&P of Lydia's marriage being published in the newspaper, even though it was not done "properly", as her mother said!