It is a book designed and created to attack Ulfrics personality and spread libel. So there is no need to talk about the civil war since what he is acused of doesnt hapen during civil war but before.
This is simply a fabrication of your mind. The book is a historical account of what happened at Markarth written by a scholar irrespective of your inability to recognize that fact. It's lore and canon for the facts to which it speaks because it stands completely uncontradicted by any other content in the Elder Scrolls universe. Lore content isn't arbitrarily rejected just because a player doesn't like what it says. If that absurd basis was applied we would have almost no lore at all for the games. If you want to pretend in your own roleplay that lore documents are false that's your prerogative but in a discussion about what actually is lore from the games such assertions are invalid.
Ulfric killed everyone in Markhart, Nords and Bretons, only those who fought with him remained.
First of all the people remaining in Markarth were not only those that fought with him. The book says
anyone that didn't support him was executed not
everyone. It's a criterion. It's evident when you read the passage that follows that it was an ongoing process and the reason why the Imperial Legion assented to his demand for open worship of Talos in the city was so that it could reclaim the city from his men and put an end to the mounting death toll each day as he executed more and more people.
Second of all that took place
24 years ago. The city has since largely repopulated.
It is imperial propaganda, created to be a book equivalent of "Nords arrise!" to mantain the discussion as a gray area.
It takes a truly distorted perspective to draw that kind of conclusion. It's not even remotely equivalent to
Nords Arise! That book purports on its face to be a Stormcloak recruitment essay, i.e. a self-professed opinion piece, and not a historical accounting.
On top of that the few facts it observes are accurate, i.e. that High King Torygg accepted the terms of the White-Gold Concordat during his brief reign, the Aldmeri Dominion waged war with the races of men, Saarthal was sacked by the Falmer, and Ysgramor and his army of Companions returned to wage war on them and cast them out of Skyrim. Nothing in the book is
libelous (for your edification slander is the term for oral defamation, libel is the term for written defamation) either so even if one were to accept your completely incorrect statement that the two books are in anyway similar in nature it still doesn't support the notion that the contents of The Bear of Markarth are in any way untrue.