While the author of "The Bear of Markarth" is certainly in favor of the Forsworn -- by which I mean that the author believes that the Forsworn are generally demonized and he wishes to paint them in a more neutral light, similar to how a modern author might attempt to defend native practices considered "barbarian" by calling them part of a unique culture -- there is no suggestion that his information is innacurate.
Igmund flat out contradicts it when he states he was the one that offered the free worship condition. It IS inaccurate.
The book states ALL forsworn officials were put to death, yet Nepo and Madanach remain.
Less certain, but still pretty strong evidence is Thonar's journal where he notes he should have let Igmund execute Madanach instead of imprisoning him.
This isn't even the first time the empire's written propaganda. But this subject has nothing to do with the civil war. It's about the forsworn. We do have records on their past actions(The nords took over the land relatively recently, and they acted exactly the same before that happened), and they've generally been unkind to everyone that goes into the reach.