After the kidnappers kill the trooper and then one chases after the 2 eyewitnesses you can see that they are on a straight road (no turns and he catches up to them fairly quickly) but the next morning when Marge arrives on the scene of the 2 bodies she arrives from the direction of the trooper's body (the first shooting). After examining the bodies of the eyewitnesses she asks her deputy "where the trooper is" and the Deputy points in the direction she just came from and states "down the road a bit" how did she miss it? She would have had to have driven right past the trooper's crime scene to get to the 2 bodies.
The movie wasn't based on a true story. The Coen brothers just threw that in for whatever reason.