Is it unthinkable that the Federal Bureau of Investigation would spy on a presidential campaign for political purposes? I can personally attest that it has happened before—during Barry Goldwater’s 1964 campaign.

Every poll agreed that President Lyndon B. Johnson would easily win the election against the conservative Sen. Goldwater of Arizona. But LBJ wanted a landslide so he could implement his Great Society vision without resistance and go down in history as one of America’s greatest presidents. For Johnson, extremism in...