I would imagine they'd pretend the phone lines are down with the weather for the first few weeks to give the directors time to skin out to the new Bermudan Headquarters
Seriously though, you can imagine they'd be doing everything in their power to avoid paying out, by looking for ways to lay the blame elsewhere. But usually these payouts go all the way to court, and even then the insurers would be underwritten - sort of insurance on insurance - just hope the sucker at the end of the chain isn't AIG
Cheers,