Likely, the Apache and other hunter-gatherers in times past caught rainwater. At City of Rocks State Park in New Mexico (north of Deming), that's just what they did. It may be also that water collects sometimes in between the rocks, in the shady spots.
There's also the wash on the north side of Indian Bread Rocks. Maybe water can be dug there. Worse case, Apache Spring is only an hour or two walk south of there.
I noticed shallow circular holes about 6 inches across dug into the rocks in a bunch of places, and they had about a half inch of water in them. I don't think it's rained here for days, so I'm guessing it's condensation from the cooler night before. What do you think?
Check out the video. Those are the metates, or grinding mortars, that give Indian Bread Rocks its name. They used them to grind acorns, mesquite, prickly pear seeds, etc. But yes, they collect water, too.
At City of Rocks, there are skinny channels to collect runoff from some rocks. I think they'd put vessels where the channels drained.
Awesome video, thanks for sharing that! The hole he found water in is exactly like what I saw. I saw a big wash on my way down the mountain. I might go see where it leads.