Do Schools Kill Creativity?

In this video he talks about how you don't grow into creativity you grow out of it. We are born creative and education destroys part of that creativity. If this is true, if we are putting restrictions on student's creativity then what possibilities are we taking away from them?
I feel as though it depends on the teacher whether or not we are destroying their creativity. If a teacher is allowing them to really think and come up with solutions on their own and projects that can relate to the material then I feel as though they can help that creativity survive. Sometimes as a teacher we are required to put restrictions on our students to help them progress, but I feel as though there is a way that you can do this without destroying their deep inner creative thoughts.