In the minutes after a cascade of gas explosions crippled the Deepwater Horizon on April 20, confusion reigned on the drilling platform. Flames were spreading rapidly, power was out, and terrified workers were leaping into the dark, oil-coated sea. Capt. Curt Kuchta, the vessel's commander, huddled on the bridge with about 10 other managers and crew members.

Andrea Fleytas, a 23-year-old worker who helped operate the rig's sophisticated navigation machinery, suddenly noticed a glaring oversight: No one had issued a distress...