The table festooned with red “Carly for America” placards arrived hours before the candidate. Political operatives took up positions outside the front door to catch supporters of Carly Fiorina, the corporate executive-turned-Republican contender, and gather their contact information before steering them inside to the room where she would speak. But the table, the placards and the workers didn’t belong to Mrs. Fiorina’s campaign. They were there thanks to the “super PAC” supporting her run for president. The Federal Election Commission forbids direct coordination between campaigns and super PACs, lest candidates effectively rely almost entirely on the huge, unlimited donations of...