The dispute about Moore's age is settled in Mike Fitzgerald's excellent biography on Moore. He is listed as born in 1916 in the 1920 cencus.
I don't know why some sources haven't updated their records yet.
What's more strange is that Moore's mother was off by three years as to when she gave birth to him
There are plenty of other fighters who's age is still in dispute. I don't think someone has nailed Sonny Liston's actual age. The last documentary I saw on him the placed his birth in 1927 or 1928. Liston's father would carve the birthdates of all his 25 children on a tree near their house, but one day the landowner chopped the tree down and all the birthdates were lost. Add to that, Liston's father was a drunk and habitually cruel towards his children and might not have given a shit when their exact date of birth was. The census that states Liston's birth year as 1932 could be well off.
Liston certainly always looked significally older than his given age.
Another fighter whose age was always in doubt was Dennis Andries. Supposedly he had no clue hao old he was and kept giving the same age for years. At one press conference a reporter confronted him with this fact and asked which year he was born. Andries paused a moment and replied "I'm 35 years old".
Joe "Old Bones" Brown, one of my favorites, is recorded with different birthdates all depending on which source you use.
There are probably many more.
-KOKid-