I finally got around to watching the original Planet of the Apes and the first thing Heston and his team do, after deciding there is no life, is to march into the desert away from water. Why do that? Isn't the first rule of survival to follow the water? Do any commentaries ever touch on this?
The longer version answer:
They came down into what appears to be a large high desert lake with another lake at about the 11:00 position as viewed through the pilot's window. The earth date according to the ship's monitor was reading Nov. 25, 3978.
As they scramble out of the sinking spaceship, the camera shows a partial panoramic view of what looks like a very large lake with no apparent outlet. The canyon they paddled their raft through was actually just a connecting channel between adjoining lake sections.
Later in the movie a still bandaged Taylor is trying to communicate with Zera and Cornelious about where he came from. They produce a map that shows the supposed 'lake' in the forbidden zone where his ship sank. As he traces his overland route for them you can clearly see that the lower western end of the lake narrows, twists and turns through a gorge until it eventually drain into the ocean.
If they would have taken that water route through to the ocean, they would have discovered no civilization and likely died of thirst. Luckily for them, the route they took was actually the shortest possible route to food, water and civilization.
I just found this production background data: