Admiral Byrd, now dead, cannot refute any of the stories being spread about extraneous activities during his trips to the South Pole. The famous story about his widow having a sudden change of heart and pulling a letter from his coffin, handing this to his grandson, is now firmly in UFOlogy lore. Admiral Byrd did not have contact with space ships or trips to underground cities, but disproving the proposition is unlikely to happen. Any change of heart on the part of family members is likely to be interpreted as dithering, as the widow already indicated dithering on the letter. We are to assume that she wanted the secret to go to the grave with him, and dithered at the last minute. If she was carrying out the Admiral's wishes, the letter would have been destroyed. If it was her decision to destroy the letter, contrary to his wishes, she would have destroyed it. The scenario shows dithering, presumably on everyone's part. Therefore, this is a safe story, as the proposition can not be disproved. Like the MJ12 papers, a good forgery, the log might be examined but would be inconclusive in either direction. Safe.
Given that, why would someone want to concoct such a story, and go to the extent of enlisting family members of a famous man? Where the Men In Black do indeed live secretly in underground caverns on the Earth's crust, there are no other cultures living in such a manner. Like the fantasy in 20,000 Leagues Under the Sea, the concept of living in bubble cities under the ocean or warm and well lighted caverns intrigues humans as this is an expansion of their living space. Humans trudging through rain and snow, picking up after tornadoes and hurricanes, and dealing with skin cancer find relief in this fantasy. However, in the context of the alien presence, the intrigue goes beyond this diversion. Humans hearing threats of a mass landing, which we have explained would not be allowed to occur, have their anxieties lessened by such stories of secret cultures already on the Earth. Heck, why worry, they're already here! With a sign of relief, the populace is supposed to come to the realization that cohabitation has not harmed them to date, so there is no need to worry. An elaborate tranquilizer.