Best House of the Dragon analysis I've seen is that the book is written within the world as a history and is therefore the "accepted" version of events (not necessarily how things went down). The show is clearly leaning into this notion, for better or worse. Mostly better imo.
Ex: Book apparently tells of Aemond's attack and murder of Luke as deliberate, while HotD shows Aemond losing control of Vhagar to a degree (thereby "accidentally" starting the war). Because Aegon is remembered in-world as a sociopath, book interpretation would also make sense.
To expand on this example, only recounting of events from neutral parties would be what happened at Storm's End prior to Luke and Aemond leaving. Only Luke (dead) and Aemond (doesn't care about the history books) would know how the death actually occurred. Show tells that story.