Not looking to pick a fight but that sounds like folklore to me. I can believe in evaporative cooling but that only provided a refreshing drink for the people in the car. If anything the bag might have blocked the air to the radiator, but then again, if the car overheated they had some water to put in the radiator.
You are correct. That was the proper use of the bags. They were soaked with water on the exterior and hung so aa not to block air flow to the radiator. The evaporation kept the water cool for drinking. We also hung a bag on the island at my friend's desert gas station to keep cool drinking water for us when working on our cars.
That's what I remember. They were canvas so that a small amount of water would seep through, keeping the canvas damp. Otherwise, they would have dried out after a few minutes on the highway on a warm day. Turns out they've become a collectors' item.