Ivies do give aid, just not how you think. (More on Ivy poaching.)
For example, certain programs will turn your loans into outright grants.
e.g.
Columbia
http://www.studentaffairs.columbia.e...lars/index.php
Penn Vagelos (Biology)
http://www.sas.upenn.edu/biochem/vspmls.html
Cornell (Tradition)
http://www.commitment.cornell.edu/tr...html/main.html
Cornell (Meinig National)
http://www.commitment.cornell.edu/CNS/index004.html
In another sense, you will be given research money or access to better classes, research programs, etc.--aid (in my mind) of a different sort:
Penn: University Scholar, Benjamin Franklin
http://www.upenn.edu/curf/uscholar/
Cornell:
http://www.commitment.cornell.edu/CPRS/
Cornell (Mckinley):
http://www.commitment.cornell.edu:16080/mck_site/
Stanford, not Ivy but:
http://www.stanford.edu/group/ps/
I know this isn't what people first envision when talking about aid (i.e. making these expensive places affordable), but these programs seem pretty awesome if you can get in one.
I'm sure there are others I don't know of . . .