I offer the hypothesis that the function of the repetition of these quotes down the years has been to signal tribal affiliation.

Your hypothesis seems clearly true to me, and I have thought of it myself. However, with these quotes, I was really unable to figure out which exact bad-faith misinterpretation was being suggested. (Admittedly, as I note in my response to Joshua Z., my own original interpretation of the Bush quote may have been too favorable, though even in that case, it still requires a hostile over-stretching to make the quote a remarkable exhibit of irrationality.)