Well my Doctor told me that if you really want to be a doctor, you can become one anywhere. I think it's quite true. But getting into the residency of your choice, now, that is a different story. Those are years of your life that you just don't want to spend somewhere you don't want to be. So in that case, going to a big name school does make a difference.
But in the end, once all the bureaucractic baloney is dealt with and you are working in the real world, it's all up to you and not to where you went to school. If you were a lawyer, you'd have more of a likelihood to get a crappy job unless you went to a big name school. But a doctor? Nah.
Mr. 😡