Its all about money, honey!!
I came across this article on the web, thanks again to Delip. Its by some MIT professor, Phillip Greenspun. He has wonderfully articulated how Ivy League universities, and in particular MIT decide on the tuition fee waivers. Though the article itself is about 8 years old, some of his suggestions seem to have been implemented in the form of the OCW. And after you finish reading the article, do not forget to look at the MIT graduation 1998 pics. They are interesting!
After reading the article, and also from some other related snippets of information, it is quite evident to me atleast, that if you are ready to pay the full tuition fees, and are financially sound (actually ultra-sound), you can easily walk into the Ivy League, with just a modicum of aptitude.
Final word: Money can take you to Ivy League, but not to IIT!!