The money was all appropriated for the top in the hopes that it would trickle down to the needy. Mr. Hoover didn't know that money trickled up. Give it to the people at the bottom and the people at the top will have it before night, anyhow. But it will at least have passed through the poor fellows hands (earliest source I've found, March 22, 2012).
The meme isn't new (it's been around almost three years, at least) but the quote is mostly accurate (it's missing ellipses). However, important context is also missing, context that places this observation slap dab in the middle of the Great Depression (to talk like Will Rogers, just a little bit).