What I mean to say is, while there might be at least some inspiration for the stories, in the vaguest sense of the word, from real occurrences in post-Roman Britain during late-Antiquity, for all intents and purposes, they are simply stories, and certainly not reflections of any sort of accurate record of history.
But to someone reading or being told these tales from "Historia Regum Britanniae" or later Arthurian Romances of the 12th and 13th centuries, was there a sense of understanding that they were fanciful, or was there some degree of belief in the historicity of what was being related? In short, would Arthur be taken as fact, fiction, or something in between?
Ooooh that is simply a fantastic and also terribly intricate question. I'll approach it from my interest in textual communication and my side-interest in the idea of 'fiction' in the Middle Ages, just so that you understand what background I'm working from, but I'll try not to dip in too much jargon! (Social historians or literary historians will probably have different answers!)
Now, I'll take you back a bit further to understand how 'fiction' may have been understood in the Middle Ages. In the fifth century, Macrobius' commentary on the Dream of Scipio is key: in this text, Macrobius details how something that is obviously untrue and unfactual, may still carry a message to be understood. Sometimes, texts are written as complete fancies, without any lessons to be drawn from it. However, sometimes a lie can be told to show a truth - and this is where it gets interesting. Moving up a bit in time, Bernardus Silvester and Augustine were also concerned how certain types of texts - fables, romances, myths - may clothe the truth in a lie to make it more palatable for a wider audience.
On to Arthurian literature: many writers, poets and minstrels found themselves with a bit of a problem. How do you present narratives with magic and adultery to your good Christian audience, and do you choose to present them as reality? Several solutions were found. A big one is 'fingierte mündlichkeit': 'feigned orality'. Somewhere, the author heard this story, and presents it to his audience. A related one is the 'reliable source': one of the characters in the story left some writing behind, and the author has found it. In other texts, you'll find the poet insisting that although there are many lying minstrels, his version of the story is the only good one, thereby discounting other forms of literature and showing that some research has been done by the composer. Or, you have poets like Chrétien de Troyes, who introduced the adulterous Lancelot-Guinevere relationship, explicitly stating that this bad bit was inserted on the behest of his patron but hoping that his audience will still enjoy the narrative.
What do these 'solutions' mean then? Well, poets, authors and composers were aware that not all elements of their stories were factual, and that there were many versions on common Arthurian themes. However, for their own sake, it was in their best interest to sell the stories as something that contained a kernel of truth. Chrétien de Troyes asserts the power of chivalry and love, Marie De France's romances depict the loyalty of a knight, and Malory's Morte Darthur is an excellent example of how the relationship between a king and his retainers can erode through treachery. The dragons, damsels and quests may not have happened and are thus lies but they cloth the truth that lies behind these noble concepts. While the vast majority of Arthurian stories pleaded to tell a truth, they were most likely understood by the audience to be a pleasant cover to understand a fundamental truth.
Walter Haugh, Vernacular Literary Theory in the Middle Ages: The German Tradition, 800-1300, in Its European Context Walter Haugh, Die Wahrheit der Fiktion: Studien zur weltlichen und geistlichen Literatur des Mittelalters und der frühen Neuzeit D.H. Green, The Beginnings of Medieval Romance: Fact and Fiction, 1150-1220 Minnis and Scott, (ed.), Medieval Literary Theory and Criticism c.1100-c.1375: The Commentary-Tradition A. Hüttig, Macrobius im Mittelalter: Ein Beitrag zur Rezeptionsgeschichte der Commentarii in Somnium Scipionis Uta Störmer-Caysa, Grundstrukturen mittelalterlicher Erzählungen: Raum und Zeit im höfischen Roman