There's no obligation to believe or not believe a source. There are the facts and then there's the interpretation of the facts, the latter is what constitutes history.
The crux is that the interpretation doesn't happen in a void. It's always driven by context in which a record first originated. Historiography isn't just about creating new narratives, it's also re-interpreting existing narratives within their context. Which interpretations of the past exist? Why did a particular narrative become dominant? What motivates historical actors to promote one narrative over another? To what extent are establish facts corroborating with an generally accepted narrative?
For instance, Caesar's De Bello Galico isn't an objective, factual account of his famous campaign to pacify Gaul. It's a textbook example of a narrative of the facts that served different purposes. Here we have a roman warlord who wants to capture the story for posterity, but also leverage his report as a propaganda and finally as an apology geared towards the senate and his enemies.
That doesn't mean we should dismiss De Bello Galico is a worthless account. Its value isn't in gaining a facts based perspective of the different cultures that populated Gaul some 2.000 years ago. Instead, it's an unique insight in the mind of a roman general and what motivates him to write a particular narrative.
Then there are the biases and opinions of the contemporary historian interpreting De Bello Galico today. That's where it gets interesting. The art / science of history is akin to watching the past through the back mirror in your car: perspectives and interpretations change as more time and distance passes by, as well as the mirror itself warping the image over time.
Ultimately, we are all slaves of the arrow of time. The idea that we can somehow capture the past in excruciating detail is almost predicated on the fact that you have to pretty much build a static, frozen version of the Universe at a particular moment in time. That's - of course - science fiction. So, when looking at the past, one has to always give countenance to the fact that you'd do so through the imperfect proxy of historical records, the fallible memory of eye witnesses and a sampling of artifacts. There's just no escaping that reality.