That quality doesn't seem to exist. Fulbrighters have all the same 'life-changing' experiences that other study abroad students have. A few of them mentioned the prestige of the name as an added benefit, but for the most part, their experiences were like so many others I've already pored through. Their essays were interesting, but they seemed to all have the same sort of epiphanies--and they couch them in the same terms.
The first 'epiphany' is the idea that being abroad helps you understand your own country better.
"I discovered that it is very useful to view one's society and its institutions from afar." (Experience, p. 87)
"I began to know my own country better." (Experience, p. 119)
"My own understanding of American literature has been broadened, and my commitment to American traditions and institutions has been strengthened by the Fulbright experience." (Experience, p. 171-172)
"The Fulbright experience has led us first to what might be called the otherness and strangeness of the other; but this experience in turn has led us to wonder more about the onlookers themselves, which is to say that we now have a more intense wonder about, a sense of strangeness concerning, ourselves, Americans, as a people." (Difference, p. 383)
"The Fulbright gave me a chance to explore more fully what people are and what culture means...Ironically, while gaining what is Iceland I also have found a better milieu for expressing my Americanism." (Experience, p. 296)
There's actually nothing ironic about it. Irony is a discrepancy between what is and what should be--and after reading the same reports from all the other Fulbrighters, it seems that being in another country should aid the personal expression of Americanism, should teach the participant more about his or her own country.
It makes perfect sense to me. How can you know what your culture is if you've never compared it to any alternative culture? It's not an epiphany, it's just reflexivity...