I don't know the figures for large universities, but at the small liberal arts college I graduated from and the one I've worked at for the last 15 years, the average figure for "full pay" students—which, as the name suggests, is the students who pay, or whose families pay, the full sticker price, either directly or through loans—has generally been between 46% and 53%.

Now, if you have figures showing that what you claim is true on the whole across all of US higher education, please, by all means, post the links. I'm genuinely interested to know just how different it is with the larger universities.