As in Alpine climbing, they may have felt that using protection would slow them down too much to get to their destination on time. Its a long trail. From a climbers point of view it ain't nothin - I've been in a LOT worse places without a tether. Your body does get used to the exposure and stops puckering on its own. After while there is no body fear left - just careful movement.

Not that the movie isn't awesome, but its a walkway afterall, maybe a deteriorated one, but its no polished granite slab.
Jim