Statements in the interview text by both Bronso and the Qizarate priest indicate that Paul-Muad'Dib and Chani are both still alive and Emperor. Both also refer explicitly to Bronso's Analysis of History, and do so more than once.
The problem is that the Analysis excerpt reads as though written years afterward. It begins
Muad'dib's Imperial reign generated more historians than any other era in human history. Most of them argued a particular viewpoint, jealous and sectarian, but it says something about the peculiar impact of this man that he aroused such passions on so many diverse worlds.
Towards the end we read
Other histories say Muad'dib was defeated by obvious plotters—the Guild, the Sisterhood and the scientific amoralists of the Bene Tleilex with their Face-Dancer disguises. Other histories point out the spies in Muad'dib's household. ...
And still later
Yet, they delineate the Qizarate cabal guided by Korba the Panegyrist. They take us step by step through Korba's plan to make a martyr of Muad'dib and place the blame on Chani, the Fremen concubine.
Can anyone come up with an explanation or timeline that allows a historian to be condemned to death during Muad'Dib's reign for a book that isn't written until after his reign is over?
Besides, of course, the "erroneous in-universe texts (of historians)" interpretation that would require the content of both texts to have been altered.