That maybe so, or may not (I haven't read the full paper, thank for the share!)
But a ten year old paper published in Econometrica using fuzzy regression discontinuity investigating school outcomes in Boston and New York city is unlikely to sway opinion of parents who send (or try to send) their DC to schools like QE boys.
Most parents base their decisions on perceptions, personal experience, 'gut feeling' and what other parents are doing. Going by that, for many, having their DC in a motivated peer group with low class disruption is desirable. Most people don't live by econometrics article.
That said, the article itself is less clear cut in its conclusion (like most good papers of this type are). Copying from the paper (emphasis mine)
Of course, test scores and peer effects are only part of the exam school
story. It may be that preparation for exam school entrance is itself worth-
while. The RD design captures the impact of peer composition and possibly
other changes at admissions cutoffs, while ignoring effects common to appli-
cants on both sides. Likewise, unique features of an exam school education
may boost achievement in specific subject areas. Students who attend Boston
Latin School almost certainly learn more Latin than they would have other-
wise. The many clubs and activities found at some exam schools may expose
students to ideas and concepts not easily captured by achievement tests or our
post-secondary outcomes. It is also possible that exam school graduates earn
higher wages, a question we plan to explore in future work. Still, the estimates
reported here suggest that any labor market gains are likely to come through
channels other than peer composition and increased cognitive achievement.
Can these results be reconciled with those of other studies reporting a strong
association between group averages and individual outcomes? Every context is
different, and the absence of peer effects in one setting does not prove that
such effects are unimportant elsewhere.