The retreats I give almost always involve inviting people pray with scripture. Inevitably, there are some people who have difficulty with their prayer because they become obsessed with certain factual details of the story. What month was Mary in her pregnancy when she left Elizabeth? How could Jacob really wrestle all night long with God? Was Joseph still alive during the wedding feast at Cana? And so on. The problem is that if the retreatants are spending time worrying about factual details, it is hard for them to engage the material in a deep way, it is difficult for them to hear God speaking to them through their encounter with the passage they are praying with.
I read in a book review in a recent issue of Commonweal what I thought was a good description of what I hope retreatants and others can do when they are praying with scripture to avoid this obsessive tendency. Paul Lakeland writes that one way to approach the Gospels is
simply to let the text wash over us, to encounter the plain text in a kind of second naivete that has left behind both childishness and the professional suspicion of the exegete. What we need is what the historian David Emmons has called “a hermeneutics of affection,” a willing surrender to the charms of the story.
The approach recongizes that there is insight to be gained from our encounter with the Gospels (or any other biblical passage for that matter) that is not dependent on factual accuracy or our getting all of the details. If we can let go of deep analysis of detail and simply “let the text wash over us,” we can open ourselves more easily to what God wants to reveal to us in our prayer.
Creo en Dios! 
Phyllis Tickle loves to tell a story that goes something like this. She was doing some sort of presentation with a group of folks about the Annunciation. Many of the adults in the room were struggling with the story, obsessed as you say, with the details and whether or not the story was true. After her talk, one young man came up and said to her “I don’t get what they were arguing about. The story is simply too beautiful not to be true.”