You might want to look up what happens in Yuma and the Imperial Valley, where it can be even hotter, because 1000ft lower elevation. People have been farming the Salt River and Gila River valleys for many centuries. I see that wikipedia has got a nice article on the Hohokam people, and the large scale network of irrigation canals they built.

Not much happens in the summer, that's true, but since all SW ag is irrigated, a lot is grown during the rest of the year.

Now I can't stand Sonoran Desert summers, not possible to be outside comfortably, but a lot of people really like the rest of the year there.