Americans think Oxford is the epitomy of higher education. A lot of Americans think it's superior to Harvard as the best university in the world. I guess it has a lot to do with the idea of it being old and British. Your average American will have never heard of Cambridge, but students in College will have obviously heard of it.
What surprises Americans more though, is that Harvard is so reknown and reputable overseas. Atleast for me, I has always known that it was recognized internationally , but I didn't know that it was practically considered the best until I met more international students.