The sinking of the Deepwater Horizon drilling rig, which triggered the spill spewing oil into the Gulf of Mexico, caught the energy world by surprise. The operator, Transocean Ltd., is a giant in the brave new world of drilling for oil in deep waters far offshore. It had been honored by regulators for its safety record. The very day of the blast on the rig, executives were aboard celebrating its seven straight years free of serious accidents.

But a Wall Street Journal examination of Transocean's record paints a more equivocal...