FBI directors don't make a habit of breaking bread with organizations their agents may soon be investigating, perhaps even closing. Robert S. Mueller III, however, is about to make precisely this blunder: On June 28, he is scheduled to deliver a lunch talk to the American Muslim Council. Mueller accepted this invitation, his spokesman Bill Carter explains, because the FBI regards the AMC as "the most mainstream Muslim group in the United States." The AMC does indeed seek to convey a message of moderation. Its event this month, for example, is reassuringly titled "American Muslims: Part of America." AMC also...