Connie Britton got over it a long time ago, the part that got away. But it’s a good story, and she still tells it with feeling: The year was 1995. Edward Burns, who had just directed her (and starred in) “The Brothers McMullen,” reached into his backpack one night over dinner and handed her a script that Cameron Crowe had sent him to read. Burns wasn’t interested himself, wanting to act in his own films instead. But he thought Britton was perfect for the romantic lead.