Priorities are generally set by YOUR situation, not someone else's.
Summer in the desert, water may be your first priority, but you sure could use some shade so you don't accelerate hyperthermia. Night temps in some places can drop from 105F to 50-55F, so you can still die of hypothermia, esp if you're dehydrated. In these conditions, you'll need both water and shelter.
If you've been drinking steadily (the water in your body is more valuable than the water in your bottle) because you planned to be out for only 3-4 hrs on a lovely 75F day, and suddenly realize that you're not where you should be, the situation has changed, and you have to allow for that. Now your water bottle is empty, you're starting to feel thirsty, the sun is getting low, and you're looking at spending a night in a canyon where the temps may drop into the 30s or 40s. Your priority needs to change from water to shelter. You can stand being a bit thirsty while you find or prepare shelter. When you've taken care of that, THEN you can look for water. But since you've been drinking as you walked, your water levels won't be that bad.
The point of determining survival priorities is not to make decisions in a panic, or from kneejerk reactions to the situation you've found yourself in. When conditions change, you have to change with them. Trying to force the old plan to work can get you into far more trouble than if you stop NOW, and just think.
Sue