I wouldn't agree with that in most circumstances, but I can see where a modification of that might be necessary, or at least beneficial in unique conditions.
Chickens originated from places where it is normally very humid in the spring and summer. When a hen broods in a humid environment, the eggs loose a certain amount of moisture during incubation -- enough to create an adequate air cell in the egg so that the chick doesn't suffocate during hatching, but not so much that the chick is saran wrapped in the membrane and sticks in the shell. You really need that happy medium for a chick to hatch properly. As chickens developed in this humid environment, only the eggs with the right shell porosity hatched, so that specific trait was naturally selected.
Then humans got involved. We imported chickens to all areas of the world, many of which have a very different humidity than where the chickens perfected this egg porosity/air sac/air humidity relationship. Luckily, chickens are very adaptable and have done quite well under a variety of conditions, but there are certain extremes that are more difficult to compensate for than others. I suspect extremes in ambient humidity can cause great challenges to hatching chicks. Since chickens breed so well, in all likelihood shell porosity has been naturally selected to minimize moisture loss in naturally brooded birds in dry countries, and maximize moisture loss in birds in wet countries, but those small changes might not be enough during extremes in humidity.
Years ago I read that successful chicken keepers in some country (I can't remember which one, but it was a hot, dry place) in the 1800s would routinely set up special nests for their broodies. They would dig a 6-12 inch deep hole in the ground, line it with clay, fill it with sand, then put soft nesting material on top of that. Every few days they would add water to the sand under the nest. The idea was that the clay lined sand would hold the water for a while, the broody covered the "container" to keep the humidity on the eggs, and the hatch rates were quite high. It makes total sense, and is quite ingenious, considering all the air cell monitoring, egg weighing, and humidity adjusting we do when we use an incubator. I remembered that so well that when I had my first broody hen this year I called my broody-experienced friend with great concern, wanting to know how to do this when I planned to have my broody pen in the barn that had a concrete floor. After she got done laughing she reminded me that I live in western WA, where lack of moisture is rarely a problem.
But I can see where chicks might be more challenging to hatch in the heat and dryness of Mexico, and why someone would come up with this solution to compensate for the need for higher humidity. My concern for this method, as opposed to the moist sand trough method, is that water is put directly on the eggs. Water can wash off the bloom on the egg, which is the thin layer of oxygen permeable "sealant" that prevents most bacteria from getting through the shell and infecting the embryo. That is why eggs collected for hatching should not be washed at all, even if they are visibly soiled. There was also a discussion on this thread recently about cleaning eggs that are soiled during brooding. The conclusion was that it is best to just wipe the eggs off instead of wash them, even though wiping leaves some debris on the shell, because the bloom is that important to the health of the chick. So while I can see that soaking eggs in warm water might improve your hatch in very dry environments, it could simultaneously decrease your hatch if eggs became infected because the bloom was compromised. In all likelihood, it improved hatch rates for those that had everything very clean, but decreased hatch rates for those that had excess bacteria on the shells, in the nest, on their hands, in the water container, or in the water. So this method may do well for some, but is a huge risk. If additional humidity was needed, I would prefer to put water on the lower layers of the nest, but keep the eggs dry.