They didn't write a theory of history, or tell us that they don't care about facts, so it's hard to know. In fact, the author of the gospel of Luke explicitly does tell us that he cares about facts, and that he's writing this gospel to supplement the other accounts and make them more historical. But there are still all kinds of literary and religious features of the gospels that aren't explained by that, not to mention that early Christians, with a few exceptions, didn't seem to mind the inconsistencies between gospels very much.

One way to understand this is through the academic debate about what genre the gospels are. For example, some elements of them seem to fit the Greek genre of history, or of biography, of tragedy, and so on. If they matched one of those genres exactly, then scholars would be able to use our knowledge of that to understand what the gospel authors cared about. For example, in some ways, the gospels are the story of the downfall of a strong, widely admired man who then dies in agony. That sounds kind of like a Greek tragedy, so we might be able to say that they cared about what the authors of Greek tragedy cared about, mostly evoking emotion in the audience. But then, of course, he comes back to life, so the genre doesn't quite hold.

The other complicating factor is that Greek biographies weren't historical the same way ours are. They were mostly descriptions of great men, with the goal of teaching the reader some kind of life lesson. That describes the gospels fairly well too, and gives some indication of what their authors might have cared about, in addition to the facts of Jesus's life.

I'm only going to be able to answer part of this question, but hopefully it will get you going in the right direction. In the study of history, the idea of writing something down as solely or primarily about arriving as close as possible to some sort of objective truth is a relatively recent one in the West, and has a lot to do with the changes to how Westerners think about everything as a result of the scientific revolution that has been ongoing since the enlightenment. So while an author was trying to report events, they were also often consciously trying to push a worldview - if you look at Herodotus, for instance, he often has a moral at the end of any particular story he is telling. Even into the modern era history writing has had a significant moral quality - Gibbon's History of the Decline and Fall of the Roman Empire features prominent themes of excess, gluttony and effeminate behaviour leading to the collapse of a civilization.

There are a bunch of examples of this kind of history writing in the pre-modern era. Robert the Monk, for instance, took the Gesta Francorum, a chronicle of the First Crusade, and made alterations to it - some seemingly pointless. My favorite is that he added just a ton of severed heads that weren't included in the original text.

In terms of the gospel specifically, there is a strong consensus that they have an inter-textual relationship of some sort - that some of the gospels are based off of the text of the other gospels, and/or other sources. There is, for instance, the "Two Source" hypothesis, whereby the Gospel of Mark and another source, known as the "Q Source," which is lost, were adopted and modified by Matthew and Luke, who also added their own additions. There are literally dozens of theories about exactly how the texts interconnect, so start researching the "Synoptic Problem" if you're interested in exactly the content of those theories.

The more important point for your question is that for much of history writing, the idea of taking someone else's texts, which you understand to contain true events, and elaborating on them or altering them to highlight certain aspects of that truth, was perfectly acceptable - even desirable - history. Indeed, as someone who wants to chronicle an important event, you might have several conflicting sources, so synthesizing these together into something that promotes the aspects of the story that you're most interested in or that is more important is just good history writing.

To summarize, there are several important things. One is that the very idea of a purely objective retelling of events was not the point of history for most of human... history. You were often trying to do something else at the same time - get someone sainted, show how important a leader was, or promote certain moral values. The second is that historians had access to previous texts and the idea of taking part of them wholesale and altering them wasn't frowned upon - it was just part of the writing of history.

EDIT: I also don't mean to imply that modern history writing is without agenda - because it certainly isn't. But more and more as time goes on historians try to frame their work as relating to objective truth, which is an idea that wasn't nearly as powerful throughout most of Western historiography.