If the question is past history, I don't see why the two have to necessarily compete. According to the Judeo-Christian mythos, the world was created in six days exactly as Genesis outlined. According to science, you had the big bang, creation of the stars and elements, seperation, astro- and geophysics, and the world coaleced out of a cloud of dust surrounding the early sun. As far as either tradition holds, these are taught as The Truth. It's best to state it that way, but with enough wiggle room, questions, and unknowns that if the DM really wants it to have been created by cosmic, multidimensional mice, he can slide that plot in without grievously disagreeing with later canon.
Similarly with recent events. Tell things the way the average person knows them, tell things that are just guesswork as guesswork. Everyone knows that Bush won the election, that's a given, but the whys shouldn't come out that easily. Was it just because he was the more charasmatic guy? Infernal pacts? Did Gore know too much about the Bavarian Illuminati and he had to be shuttled out of the spotlight? Unless there's some overwhelming need to know, (or unless Gore starts crusading publicly about the symbology inherent in the $1 bill,) the average person (and by extension, the average character) would just know who won. And the setting would leave the fine details to the DM's twisted imagination.