I'll have to defer to "Physicist" and ThinkPlease" on details such as those....
I'm not sure about the error in either of these studies. I've never heard of the 5% standard you cite. For this article, they seem to be using .5 billion ly vs. 5%. But you're definitely right about the contradiction thingy; i.e., I should've said discrepancy instead of contradiction because even if the interval estimates do not overlap we wouldn't necessarily have a contradiction in the strict sense of the word.