One day in 1967, Erroll M. Brown, then a high school senior in St. Petersburg, Fla., opened his mailbox and pulled out a 3-by-5-inch white postcard addressed to him. It read in part, "Are you interested in going to the Coast Guard Academy?" If interested, the recipient was to check a little box and give the postcard to his guidance counselor so his grades could be mailed in. The teenager checked the box after discussing military service with his mother and stepfather. He saw the academy as a way to pay for his college education. But he didn't have the...