Basic Trope: The author claims that his/her work is factually accurate. It isn't.
Straight: The author's factual claims are counterfactual.
Exaggerated: The author's claims of true science and/or history are all the exact opposites of reality.
Downplayed: The author's factual claims are mostly correct, it's just the tiny, inconsequential details (like what color socks Abraham Lincoln wore when he was assassinated) that are incorrect or unverifiable. They may be an obvious Anachronism Stew, or apparent only to experts.
The work is written in a country with crimethink laws.
Alternatively, it touches on an issue where the zeitgeist is hostile to the facts.
Lampshaded: "And yes, I know Patty Duke was never Pope. Just work with me here.".
Invoked: The author is sending a coded message; presenting clearly untrue statements as fact jars the reader and alerts him/her that something else is going on.
"Yes, I know some people claim their history is factual when it is not. But I promise you, the reader, that the history in this book is really true". The author proceeds to give true history in the story.