Beowulf itself is not a history, but rather an epic which includes some historical figures. The purpose of blending historical and imaginary information (such as the character of Beowulf and the stories of the monsters) is to create an account of the origins of traditions and values of Anglo-Saxon culture. The genealogy serves that purpose of emphasizing that this is a poem about cultural origins. 

One thing it is very important to understand here is that medieval reading followed a tradition which assumed that all texts could be interpreted on multiple levels simultaneously. Rather than something being a history OR an allegory, it was assumed that any text could be read both literally and allegorically. Every text for a medieval reader had a literal sense, a moral sense, an anagogical (spiritual) sense, and a tropological (relating to symbols of Christ) sense. Where something did not make sense on one level, that was a sign that it should be read on another level.

Thus a medieval reader would see Beowulf's fight with the dragon as perhaps representing some great battle in the past or a king acting as a heroic leader in war time (partially historical), an example of the moral virtues of a leader willing to sacrifice himself for his subjects, an allegory of the human struggle against evil and as analogous to Christ's sacrifice on the cross. These wouldn't be regarded as alternatives, but as all present in the text and discoverable by a discerning reader. 

Often the answer lies in the framing of the question. Perhaps the major issue here is that the binary oppositions set out may not have been meaningful as oppositions for the original composer and audiences of the work.

It is unlikely that audiences would have believed the poem to be true in an absolute, scientific, and literal sense, including the details of the monsters and Beowulf's superhuman powers. On the other hand, no one would have read the work as a textbook on the flora and fauna of Scandinavia. Instead, the work would have been read in a context in which heroism and martial prowess were described in hyperbolic terms. Just as when someone now says, "I was on the phone for hours trying to get hold of a human being," or "With what Company X charges for ABC, I could pay off my mortgage," we interpret this as exaggeration for the sake of effect, so too the audience of Beowulf would have expected the author to embellish for emphasis.

Some elements of the poem are historically accurate, including characters other than Beowulf. What the genealogy and use of real characters and events leads readers to expect is that the story will describe the great and heroic nature of the ancestors of the audience themselves, as well as a sense of what constitutes the nature of heroism and moral rectitude, embellishing for effect or to make a better story. Since the poem does not claim to be a textbook or chronicle, it is not falsifying information, but instead using some historical information as part of a literary interpretation of the glorious past of the audience.