proof by contradiction? there are a LOT of foreigners who do obtain fellowships during the "first" round - e.g. I guess check like minnesota or penn or something - who clearly are not from top 20 schools...
and by top 20 schools do you mean ECON or overall UG reputation? i'm from a top 20 school in econ and around top 20 for overall UG - but my school has historically almost never sent econ phds anywhere ... so i doubt it helps.
also i'm sure being from a top econ dept does help - but i don't think being from an unknown dept hurts you enough to rule you out of a fellowshp. no foreign schools except maybe LSE, UCL are in the top 20 ... and i know people from foreign schools with funding at top us schools .. so\ i find it hard to believe ... also remember ivy doesn't mean good at econ ... or good at academics in general ... chicago, stanford, berkeley, nw, are all non ivy schools - yet are top schools overall ... i mean where is dartmouth or brown or even cornell compared to schools like the above listed? def. not in the same tier ...
as for the top 5 schools .. i bet profs at harvard like to help UGs at harvard, yale, princeton, etc .. but phds at harvard are not just from top schools ... i'm sure people associate less risk with the top sstudents at top programs - e.g. top 5% of harvard - as opposed to top 1% of unknown college A.. that's prolly what the prof meant ...