Look at Mark Zuckerberg, do you think he managed Facebook because of the superior comp-sci education he got at Harvard? No, it was because of the connections he made and the people he collaborated with. It's the same with any of the 'elite' schools, the real value is that you will either get to know some very smart people, or some people with access to a lot of money or ideally both that is the real payoff for going to such schools.
The other comments are correct that talent and a good mentor can give you what you need to build skill, and that the degree itself really just gets you into your first job with experience getting you your next job, but it's the connections these schools provide that help make the difference between getting a good job and building a world-class career or company.