That is either patently untrue or there are a whole lot of loopholes. I used to live in Phoenix more than 20 years ago and had a lawn that matched anything you'd find in Chicago. I still have about a dozen friends living in the Phoenix metro and all of them have at least a patch of lawn, not to mention the grass areas maintained by the HOA.
Also, most of those golf courses are taking advantage of 150+ year old water rights laws that no longer make sense in our current environment.