I'm very skeptical of this claim.
In fact up until a recent funding method change from the Trump Administration, most grant money was subject to "overhead"--a nebulous nonsensical accounting trick that allowed the university administration to get upwards of 60% of the dollars that are earmarked for grants. If you invent something, the school will take 70% of the revenue from the innovation. Much like VC, some big wins can power the school for years.
Actually, most highly productive research universities use the research as a prestige magnet and marketing tool to help grow endowments and keep up in the US News college rankings.
I would be great if the funding weren't so opaque. We may be able to find accounting info for the public univeristies. I would bet money that, Liberal arts tuition likely goes into administration, endowments, and campus improvements for student life (better food in the dining halls...)