No offense was taken at all! My point is that the question is readily resolved by looking at the data. By my reading of the data, it seems clear that at top schools, higher SAT scores virtually always increase your odds of admission.
You say that we cannot know if the 2300 is better than the 2180 per se, or if it's just correlated with other outstanding qualities. In fact, this is exactly what statistical inference allows us to do. To the extent that it's possible to identify the confounders, it is possible to separate their effect from that of the SAT score.