REMANSO TALISMA, Brazil — The death of a myth begins with stinging eyes and heaving chests here on the edge of the Amazon rain forest. Every year, fire envelops the jungle, throwing up inky billows of smoke that blot out the sun. Animals flee. Residents for miles around cry and wheeze, while the weak and unlucky develop serious respiratory problems. When the burning season strikes, life and health in the Amazon falter, and color drains out of the riotous green landscape as great swaths of majestic trees, creeping vines, delicate bromeliads and hardy ferns are reduced to blackened stubble. But...