I can't speak for UVa, but that quote is pure trash. Like I tell all students agonizing for the "top schools", going for higher education is like driving a car. Even if you have a REALLY EXPENSIVE, if you're a sh!tty driver, it doesn't matter what kind of car you drive, you'll still be a sh!tty driver.
Don't think about reputations, it's a waste of time. You can make any program, with any adviser prestigious it's all up to how much effort you put in.
sorry for the rant, I grew up on Southern California riding the "reputation" theme to death
Good luck