What happens if you didn't make a connection to someone you want to develop a relationship with?
Learn how to make connections if you want connections. University is a lot more expensive and a lot less effective for that.
So far as I can see, "a $200 marketing package and a couple months" isn't going to actually get you far, but if you're interesting and know how to network then dropping a few thousand for charity dinners or similar might be able to get you further for cheaper than being one of however many students at a big-name school.
If you go to college just for the education, then there are a lot of places that are very good for the dollar [1] (still though, Ivys dominate).
If you want a mix of the two, it seems as if you'd still want to go to prestigious schools. They have the scholarships, very good teaching, grade inflation, the connections to the progeny of money, and their grads are well received in industry and elsewhere. Really, a cursory look at the data does seem to indicate an Ivy or the Claremonts (though many exceptions exist[2])
[0]https://en.wikipedia.org/wiki/Human_bonding (Actually a good article to read)
[1]http://colleges.usnews.rankingsandreviews.com/best-colleges/...
http://www.reddit.com/r/AskReddit/comments/xqeol/the_preside...
$200k and 4 years, or $200 and a couple years sending letters? Btw, it's only going to take years for the President. The CEOs of F500's can be done in months.