According to the famous midrash which I used a while back as the basis for a joke, the spot of the Temple in Jerusalem was that on which two brothers, each worried about the other's livelihood, had met while secretly giving grain to each other.
On one hand, you can categorically state that historically, this story never actually occurred. (That, however, takes away none of its significance. The details of fiction are MORE important than the details of nonfiction, because they were chosen for specific thematic reasons and don't just reflect the oddities of historical reality.) On the other hand, it is clear what the names of the brothers were.
The brother with a large family was named Yehudah. The single brother was named Binyamin. This has to be the case, because the two brothers in the midrash are fictional representations of two tribes. Yehudah was the large and powerful tribe whose territory stretched from Jerusalem to southern Israel. Binyamin was the small tribe located just north of Jerusalem. The two tribes had fought several wars with each other by David's time. When David chose a spot for the Temple, he intentionally avoided his own tribe (Yehudah) and chose Jerusalem, which was right on the border between the two tribes. He did this in order to unify and create peace between the two neighboring tribes. He succeeded, as Yehudah and Binyamin remained united for the rest of Jewish history. When the more northern tribes - which had family ties to Binyamin - split off to form their own kingdom, Binyamin did not follow.
Given this historical background, the midrash becomes almost predictable. David chose a spot which would foster love between the tribes (whose ancestors Yehudah and Binyamin were brothers); in the midrash the spot was chosen because of the love demonstrated between two brothers. The midrash is just trying to shed light on the moral motivations behind the choice of the Temple location.
Reading Tanach, you find the story of David's choice of the location, but his motivations are obscure. Reading the midrash, the history of the tribes is obscure, but the moral significance of David's choice could not be clearer. Nowadays we would put this piece of Tanach interpretation into a shiur. The midrash chose to present the same interpretation as a beautiful story.
This is a good example of a general rule which helps to explain many midrashim, perhaps most of them. Taken literally, they often seem improbable (though this one is plausible, just unverifiable). But often they are in fact allegories, or else very clearly emphasize themes from Tanach. The challenge for thoughtful readers is to identify how exactly each midrash functions as a commentary on Tanach. This can be difficult. But even if you don't succeed, the surface meaning of the midrash is often informative or inspiring, so the midrash can be appreciated even without fully understanding the logic behind it.