This article is interesting, but it makes the fundamental error of assuming that the primary product of an R1 research university is education for undergraduates, which it is not. The primary product of an R1 research university is research, largely performed by Graduate Students, Postdoctoral Researchers and Professional Researchers. All of these are paid a salary of some form, some market-rate, others less-so. That's where the cost is, along with actual costs of instruments, libraries, consumables and buildings necessary for cutting edge research. Most of the funding for that comes from research grants and you can see how it represents a huge fraction of the budget in his charts. Unfortunately, all of the expenditure data that the Education department puts out combines both R1 and non-R1 institutions, so it's hard to see just how different the top 120 schools are from most of the rest. If you have expenditure data segmented by research intensity, I would love to see it.

The undergraduate education is part of the university, but not the primary part. (At UChicago, grad students still outnumber undergrads!) If you want to see what the finances of an institution that primarily educates undergraduates looks like, go to one of the Liberal Arts colleges, or non R-1 state schools, like any of the Cal States in California, or non-flagship schools in other states.