According Naughty Dog animator Jonathan Cooper via Twitter, Nathan Drake never actually gets hit by more than one bullet before dying. While enemy soldiers and mercenaries shoot boatloads of ammo at him, the darkened, red-laced screen that emerges when Drake is "shot" multiple times actually represents his luck running out after having consecutive near-misses.
Amy Hennig, creative director of Uncharted 1, 2, and 3, confirmed the tidbit. "That was the original intention," she said. "To stay more aligned with the spirit and tone of the films we were homaging."