I think we need to define history - you seem to be operating from the definition as a narrative anchored to a list of facts, but I consider history to be the collection of facts of themselves, from which narratives can be derived. If the narrative is bounded by the limits of the facts (dates, correlated recording, carbon dating, artifacts, etc.) then the resulting narrative lacks the potential for inaccuracies. If history is instead a narrative, into which facts are selectively slotted, the uncertainty rapidly reaches a point at which interpretation and belief factor into the history as much or more than dry facts.
I think the trick is requiring that the fundamental narrative of a given history be bounded by science (itself a narrative) in the sense that things are left unknown and unknowable where evidence is lacking or insufficient.
Egyptology is a non scientific, dogmatic narrative into which facts and conclusions are selectively slotted. The "prestige" resulting from British imperialists fetishizing the subject created a mythos of Egypt as some primal, fundamental expression of the beginning of civilization. This mythos is tended and cultivated in modern times by Egyptians and their cultural elites, with their interpretation of history resulting in notoriously poor handling of any science-based revision.
So there is dogmatic and narrative history, and scientific history. Things like the archeology of Clovis culture result in dry, but scientific history. Few people or institutions will encounter perverse incentives in that field. Egyptian heritage and tourism necessitate cooperation with institutions and corrupting outside influences that derogate the resulting narrative.
In the case of religion, there's a great deal of similarity and overlap with histories of the dogmatic sort and both suffer from the issue of the narrative selecting for ideologically convenient facts, instead of a self limiting construction founded in scientific principle.
The worst part is that science itself can be considered an ideology as dogmatic and fraught with perverse incentives as any other story we attach to dry lists of facts. The difference is in the repeatability of direct consequences - we can trust carbon dating, but educated guessing about culture based on parchment fragments that result in a story about thousands of people at a particular point in time has to be weighted similarly to religion or mythology in terms of factuality.
If you choose to believe in science, then everything becomes lists of facts, whether rigorously repeatable tests like carbon dating, or assertions about the beliefs and actions of people thousands of years ago - or about modern cohabitants of this existence. A Bayesian perspective on the deconstructed narratives as lists of facts gives us a methodology to navigate narratives rationally.
The difficulty is in assigning probabilities to the authenticity of a given fact, so - Lincoln 100% existed, Xenu 100% did not.
The modern narrative of Egyptian history (my own understanding of it) is probably 85% scientific or accurate, and the questionable bits are the ones that directly benefit the individuals or institutions that stand to benefit from corrupted or perverse incentives.
Holocaust denial, like flat earth and Bigfoot, is inherently anti-bayesian and requires wilfully abandoning easily verifiable dry facts and rigorously scientific information that is trivially accessible. To believe in such stuff you have to embrace an extreme of skepticism that makes navigating reality impractical at best, either believing everything from a particular authority or rejecting everything outside one's own direct experience.
It's an interesting problem, and I'd like to see a Bayesian history of humanity some day, with a rigorously bounded and annotated set of probabilities attached to every part of the narrative portion of historical stories. Maybe gpt-3 or future transformer models could eke out such a system.