I did some research and I think Miss Etiquette sums it all up in her blog post devoted to this topic:
“Saying congratulations to a bride implies that she has won something – her groom. The groom is to be congratulated for getting the lady to accept his marriage proposal. To avoid controversy, many people just extend their best wishes to the bride and the groom!”
We are to assume the gentleman chased his lady, caught her, and persuaded her to become his bride. He is to be congratulated for winning the heart of his lovely bride-to-be. He and his family should be congratulated. She on the other hand is a lovely flower of a woman and we must wish her all the best, and hope that this fellow is everything he has portrayed himself to be.
Which is kinda what I thought the deal would be. But now we both know. Party on.