That is true. It is usually very difficult to impossible to get a leadership job in a big corporation, if only because the corporation is (hopefully) going in one direction and only needs a finite number of leaders to take it there.
However, once all those people who strived for leadership roles leave the corporation and start their own startups, they're at a distinct advantage over those who slacked off the whole time because there weren't opportunities available. You aren't going to change the company, but you can probably change yourself.
One of the things I regret, in hindsight, about my college experience is that I really didn't try very hard. I thought it was pointless (which it kinda was, professionally), but I didn't realize until my last semester that I could've made it meaningful.
Peter Norvig put it well: "Be the best programmer on some projects, and the worst on others."