UN-POSSIBLE!

In all seriousness, it doesn't matter how intelligent she is. In fact, logic can easily be used to fry her brain right into that direction. Take the AUM-Shin-rikyo cult in Japan that set off a serin gas attack in the Tokyo subways a few years back. Most of the perpetrators were not idiotic back-water hicks. Most of them were top scientists at Tokyo University - a university that has a better reputation than Harvard.

Simply put, you can't get people to jump into doing what you want them to do right off the bat, but you can logic them in an ever complex maze that heads, unknowingly on their part, towards them doing things like that.

It would take a couple of months of clever manipulations on the part of a few radical muggle-borns, and of course, the pure-bloods are doing nothing to prevent it. Perhaps her parents get killed by Voldemort's faction, and as she gains prestige in the movement, and they begin prosecuting pure-bloods, she starts developing a more and more radical philosiphy and it won't take long for her to be calling for the guillotine to be erected right in the middle of diagon alley - inspired, of course, by the incorruptable Robepierre and the French Revolution.