Matt Feeny and Chris Campbell offer a vital insight into Loughner and, yes, Nietzsche:
Loughner didn't see himself as a nihilist. He saw himself as fighting nihilism. This is evident in his fixation in his YouTube videos on the idea that words have no meaning, or have somehow lost their meaning in a process of nihilistic decline—a fixation that seems to lie at the basis of his tragic grudge against Gabrielle Giffords.
So does that make Nietzsche and Jared Lee Loughner philosophical brethren after all, joined in the same fanatical fight against nihilism?
In a word, no, and Loughner's pathological fixation on the meaning of words is the giveaway. One way of looking at Nietzsche's project is that he set out to teach himself and his readers to love the world in its imperfection and multiplicity, for itself. This is behind his assaults on religion, liberal idealism, and utilitarian systems of social organization. He saw these as different ways of effacing or annihilating the world as it is. It is behind his infamous doctrine of the Eternal Recurrence—in which he embraces the "most abysmal thought," that the given world, and not the idealizing stories we tell of it, is all there is, and he will affirm this reality even if it recurs eternally.
Such an anti-nihilist does not murder nine year olds.