Three kids claimed to have seen this apparition and as far as I know, there were no other witnesses. So why do so many people believe that it really took place and was not a story that the kids made up?
This sounds like all of the UFO sightings. The flying saucers are always seen in a remote area by only one or a few witnesses. They never land in places like Times Square or the National Mall.
People believed because Our Lady said that on October 13, 1916, God would preform a miracle so that all would believe in Him. In front of 100,000 witnesses, including the local Commie authorities, the sun danced in the sky for several minutes, at the end the ground and people, both wet from recent rain, were dry, people were healed and many conversions occurred. This event was reported in local and national papers and there were photographs taken.