The problem is often that children's childhoods are literally sacrificed to that ideal of getting into UVA/Princeton/Yale, etc. This girl may have been discouraged from pursuing her actual interests (scouts, horseback riding, etc.) and instead had them channeled into things that would look better on an admissions application (chess club, afterschool Chinese) beginning in kindergarten.
Our solution was to encourage our kids to do what they loved and to think of college admissions as a crap shoot.
First of all, lumping UVA in with schools that have single-digit admission rates might not be the best move. We have always published our admit rates broken down by residency. We offered to 38% of the Virginia residents who applied this past year and we offered to 23% of the out-of-state applicants. I can't fathom UVA ever being among the 15 or so schools with single-digit admit rates.
When it comes to a student's involvement outside the classroom, we don't favor certain kinds of activities over others. With 869 student organizations are currently registered in our system, it should be pretty obvious that we value variety. I hope you'll chose to make meaningful contributions in some arena (home, school, job, community, etc) of your life.
I've heard a lot of people talk about colleges valuing long-term activities in the admission process. While it's always interesting when a student has sustained involvement, that isn't something we require. Plenty of students change their activities as their interests evolve. Also, as your academic responsibilities become heavier, it may make sense to cut pack on your involvement so you can get your school work done. I don't want you staying on a team or in a club if it's making your feel stressed or miserable. Move on to do other things!
Lastly, admission is not a crapshoot. Admission offices establish pretty elaborate review processes to form their incoming classes. It is not random. I do like that the parent who wrote the comment encouraged their student to participate in activities that they loved!