A large, commercial HVAC unit will often use water pouring over the condenser coils, or else recirculating through a cooling tower, to improve its performance. While not exactly a water waster as another answer called it, it can go through a fair amount of water pretty quickly, and without the constant water supply to keep it topped up, everything stops.
I have seen commercial HVAC solutions that had both the condenser and evaporator in package units, and water was piped around the building to cool the condensers and carry the warm water away, and I've seen water-cooled condensers that then pumped the refrigerant around the building to the various evaporators. Both are very effective, both have different costs, advantages and limitations.
But yeah, with a big commercial HVAC, a water main failure can absolutely sideline your air conditioning. But water mains are important, and the utility will have things back up soon enough.