This article is from the FAQ, by with numerous contributions by others.
No, but if you received less than $2000, you at least have a
chance. Fulbright grantees' applications have been known to be
rejected even with grants below that, on the argument that the
program itself, beyond monies expended on behalf of an individual,
push each individual above that limit. Above that limit, you can
only hope to be from the PRC, or use the other avenues described