I kinda know how phone updates work. Samsung isn't the only party... the carriers are often the hold up on releases.
BTW... I did Google it. I didn't see a Samsung "promise" on a release date. Since I don't own a Note 3 nor do I plan to, I think I've expended as much energy as I should in the endeavor. I didn't make the claim. You did. I'm not sure how me working to prove you right is in my interest.
in edit: What I found in my Google search was that the 4.4.4 update for the Note 3 was released in mid November for ATT customers.
in edit 2:
This is the first page of Bing's return on the search parameters you offered. I do not see an official Samsung link to the claim you make.