My knowledge of the matter comes only from what I studied in my high school Latin classes, so I might be grossly misunderstanding the whole subject, but I seem to recall that historiographers would often bend fact either for artistic reason, or to downright push a political agenda.
That said, if we only have knowledge of an historical event through the account of one or more historiographers, how do we know its account has not been twisted, or even fabricated?
Side note, people who study history and provide historical accounts are called historians. Historiographers study the development of the methodologies that historians use to study history and the changing historical picture through time. Historiography is meta-history, the history of history.
Your questions seems to be about historians of the time, not historiographers, but interesting that makes it a historographical question.
(Quick foreword: this is based on my experience in studying Hellenistic history, one of the most interesting periods to study in regards to Historiography.)
It may come as a surprise, but the best way we can tell the genuine accuracy of ancient historians is through consensus and critique. If we have two sources disagreeing on a basic fact, you go searching for as many historians that agree with one side or another. While this isn't a perfect system, more often than not, an accurate story is the one more repeated. This is further aided by a basic investigation on causes for inaccuracy. For example, if the historian Arrian has a different account of one event, it is likely due to the influence of his original source, Ptolemy I Soter.
At this point, we can also take in the opinions of ancient historians on other ancient historians. For example, one account of Alexanders campaigns is by Quentus Curtius Rufus. Curtius' account is well known to be heavily exaggerated. His original source is a historian named Cleitarchus. According to historians Circero and Quintilian, who had read Cleitarchus' work unlike modern historians, regarded Cleitarchus "as an able sensational writer who took the liberty of lying outright in order to produce a more brilliant account.” So it is through the consensus of ancient historians that we are able to parse out the likely cause for the semi-fictionalised account written by Curtius.
We can even see the influence of historiography on the written accounts. Diodorus' accuracy on the events of the Successors differs in depth depending on whether his original source, Hieronymus of Cardia, was present or not. Where Hieronymus was present, we get descriptions of the armies and their opinions in detail, when he wasn't we get details that are more vague.
Quote from The Archaeological and literary evidence for the burning of the Persepolis Palace. N. G. L. Hammond