I would strongly disagree that a big time school degree (Ivies as well as schools like Stanford, Berkeley, etc) doesn't pay its weight in opportunity. I graduated from Cornell in '10, and have had many doors open to me that I would never have had otherwise.
A few things make the Ivy degree worth it: alumni connections/being a recruiting destination, top notch faculty recommendations, and your peers. I'll explain further, but allow me to add a disclaimer beforehand: If you don't play to the advantages offered by your Ivy (et al.) education, you're not gaining really any advantage in life you wouldn't have had at BumF*** State.
First, the alumni connections and being a recruiting destination are the most important advantages you will have. People pursuing careers in things like finance and engineering benefit to a ridiculous degree from having all the top firms/corporations come to campus and actively pursue undergrads to groom for future careers at their organizations. My mother works for a Fortune 50 company as a top researcher and business woman, and Cornell is one of only a handful of schools in the country that they visit and recruit future 6 figure employees from, in both engineering and management areas. Her company is the norm, not the exception. Lets put it this way, if you went to Average U., how many classmates do you have working on Wall St. for a hedge fund or an investment bank earning a ridiculous amount of money for crashing the economy? Right, none. Why? Lehman Bros., regardless of what you think of them, recruits at Ivies, not Average U. The Ivy bias in some professions is blatant, and its not in professions where people earn jack, either.
As for Alumni, while a conversation started off by a statement at someplace random like "Oh, you went to Suchandsuch U? So did I!" is MUCH more likely to involve A)someone important/reasonably wealthy, and B) actually involve some passion about said school if its an Ivy versus say Boise State (example because I live in Boise). I've met about half a dozen Cornell grads in Idaho. 5 of them for sure earn 6 figures, all are in upper positions at their organizations, I'm positive all would hire me or find someone to hire me if I needed it (I'm in grad school, so moot point), and all are smart smart people. Its not only the great network you CAN tap into that's important (again, if you don't tap into it, that's a bit of a waste), but the level of alumni thats there. Are there rich alums of Boise State here? Absolutely, tons, but almost none are going to say to a recent grad "Oh you went to BSU too? So did I! What are you doing out here? [...] If you ever need someplace to get started (or get a job, or need me to make a call), let me know, here's my card." Why? Because most BSU grads aren't working in a position where they hire people. Many more Cornell grads are.
Second, your faculty will be of the caliber where they wrote your textbook, not where they read your textbook so they can teach the class, at top flight school. This doesn't mean other schools don't have specialties. If you're into a specific niche, the top researcher or faculty in a given area might be at a random school (or a big state school with a large faculty). There are lots of instances where that's the case, to be sure. That said, there will ALWAYS be tons of faculty at, or near, the tops of their niches at your top tier school. If you need a recommendation to a selective grad school, a think tank, etc., it will matter whether it came from Prof. Joe Schmoe at Whatsamatta U. versus Prof. Literally Wrote The Book on X at Ivy U. Even if you don't plan a career in academia, you will be better off in your education for having rubbed elbows with the top minds in a a range of fields at your big time school. Who would you rather have explain, for instance, sleep research in your Psych class? A prof. who has read all the research on the guy who coined the term "Power Nap", or the Prof that coined the term and wrote the book himself?
Finally, at top flight schools you have top flight peers. Sure, a disproportionate amount of them will be too nerdy to hold real conversations, have an above average chance of being an ugly girl (if female) and be exceedingly white and weathly, but god will they be smart and well connected (as a whole). Foreign dignitaries don't send their kids to Random Coll. CEOs don't send their kids (usually) to the local community college. If you think having class with people that have a great chance of dominating their field someday, or will stretch your mind, or can introduce you to someone who will do one of those first two things, is worth it, there's no place you should be other than the best schools. Say what you will about a school being what you make of it, it is a completely different feeling to be at a place where excellence is the norm versus somewhere that's got an abysmal graduation rate after 6 years.
One final disclaimer, I'm a grad student in Social Work at a low brow state school, so I'm not in a profession that cares much about my Cornell diploma and nor I didn't go to a school where I needed one to get in, and I've still been able to see the tremendous benefit. You do have to take the bull by the horns, like any other successful person, but its easier, and will get you farther, if you start grabbing bulls with a big time degree in your hand.