I agree that binary modes of thought are pervasive in the U.S. and ineptly applied to all sorts of things, including the example situation you described. Reading around on this forum, one sees daily illustrations of folks interpreting remarks as though they are "either or" expressions of thought, yet quite often a simple duality is unsupported by the remark.
I'm sure folks think they are making logical inferences and extrapolations of the ideas expressed, but that's not how one rationally develops inferences. To do that one must take what is said and carry it forward, not take what is said and "flip" it to what was not said or to what is one of its contrary ideas.
I wish I knew why folks do that, but I don't. Were I to speculate on why, I'd say they see themselves as following
George W. Bush's example from his 9/11 speech when he said one is with the U.S. or against it and that there's no in-between. I suspect that basic theme is what drives the mentality of most "average" Americans and certainly police officers, who unfortunately are not, IMO and generally, "above average" logicians.