Not only does artificial turf save water, we use water in the installation process.
After the old turf is removed and the initial layers of the installation of put down, the granite layer is watered down. After the soil layer over the top of the granite is applied, it gets a dousing of the wet stuff.
Water helps the layers compact and hold together. It also makes the various materials malleable and able to be worked more easily.
Sure, we use water now, but over the life of the installation (20-plus years) you will use a fraction of what you would with a live lawn.