Yes, that's true. I forgot to mention that, but it is now a very deliberate strategy. When we started YC we didn't even realize we'd produce an alumni network, but it is becoming more and more important.
It would be most accurate to say it competes with MBA programs. I could say with a straight face now that if you want to learn about the startup end of the business spectrum, you'd be better off doing YC than going to B school. But I wouldn't say that about college, because so much of what you learn in college is social.
Some of us have dropped out of top MBA programs (Dave and I were at UChicago) to participate in YC. And I haven't regretted my decision for a second. Most of my entrepreneurship focused MBA friends would trade in a heartbeat (and some have applied to YC). Although they are definitely selective the top 10 MBA programs take in ~5000 students a year while YC will only take ~200-250/yr at 35 companies per session.