If you mean by "begging the question" that I assuming the conclusion that extra curricular predict better academic performance, although it's true I presented no evidence, I did work with admissions at the alma-mater and the admissions department coordinated with many other selective schools to mine this data (unfortunately, it is not public data and quite old since I graduated many moons ago).
However, if you mean by "begging the question" in the more colloquial sense that I am implicitly or rhetorically raising another question about selective vs non-selective, that is certainly *not* the case. Although it's true that social anxieties are an important part of college life adaptation, the distribution of people in less selective colleges tends to be in a range where the "book-worm" really is still in the upper part of the distribution (where selective schools are picking off the outliers), and thus don't suffer as much displacement in class ranking (maybe the top person in an average HS will fall to the top 10% of a typical school, where they may actually fall to the 50% percentile or lower in a selective school).
Of course this is all averages, and everyone's experience is different, but one of the primary goals of a typical selective school is to only admit people that have the best chance of successfully graduating and being successful in life (regardless of their SAT score).
You might ask why not just admit people that pay the most tuition or some other criteria, but tuition is really a small part of the financial consideration of a selective school. It's more important to graduate people that will be successful in life later, both for prestige purposes and as a population to solicit future gifts to the institution. Being good a taking tests is not a leading indicator of this.
As others have mentioned, if you assume a normal distribution of test takers and a finite number of questions on a test, accurately measuring anything on the upper tail of the distribution is really not statistically valid (given the number of "trials" to measure the SAT score is also limited and the fact that people game the system). After some point, the measurement is really just a range. For the SAT, where there is more noise than signal probably occurs around 700/800 on a specific test (remember, SAT is also renormalized to match historical distributions, so we are talking about missing 1-3 questions over the entire non-experimental questions you are scored on. If you cutoff is lower (say 600 or so), the measurements are more statistically valid.