The company has an extra reason for making this claim, as a new article in the New York Times shows. During the horrific earthquake and tsunami that ravaged northern Japan earlier this year (and affected Leaf production, as well as other companies, to say nothing of the citizens), two dozen Leafs were severely damaged, and none of them caught fire. In fact, the Times writes, the "batteries remained fully intact, shielded by an airtight steel exoskeleton and two other layers of protection that surround the 660-pound packs." This, says Nissan North America's director of product safety, Bob Yakushi, "is a very good indication of the safety performance of that vehicle." The Leaf, along with other EVs like the Tesla Roadster and the Ford Focus Electric, use a steel cover on the battery pack. For what it's worth, the Volt's pack is partially covered in plastic. For more, you can find lots of good details over in the Times' piece.
Somewhere out there, there is a good story to be written about how the Leaf and the earthquake affected each other. This is a story that isn't done yet.