I agree this is true to an extent, and there are plenty of exceptions. Princeton, for example, has admitted a number of students with only BA's from state schools in recent years. I was just offered admission to Princeton and I only have a BA from a large state school. It really goes to show that fit, luck, and the written components (SOP and writing sample) can outweigh any kind of apparent prestige your undergrad or masters institution might lack. Obviously Ivies and other top schools provide institutional benefits that others can't (well-known faculty, prestige networks, all undergrads write theses, etc) but there's hope for state school students if the pieces fall into place. I certainly applied to Ivies assuming it was futile but found that fit and connections play a huge role!