First let's define drought. If drought is a couple of weeks without water, then the second answer is correct. If drought is typical New Mexico conditions with limited water for prolonged periods, then the first answer is correct.
Plants survive periods without water by using a couple of strategies.
However, if the soil dries to a depth greater than the roots, it has a problem. To continue to avoid drought, the leaves roll reducing water loss, but this avoidance strategy is only a last resort and the grass must be irrigated soon after leaf-rolling begins. Grasses were allowed to dry until they were wilted and brown then rewatered. Two weeks after watering, buffalograss exhibited 50 percent green coverage while tall fescue showed only 4 percent green. Zoysia grass was 22 percent green and bermudagrass was 14 percent green.