From memory (the last time this came up) That number includes staff at the Stanford Linear Accelerator (a National Lab, Stanford University Medical Center (which runs two hospitals and a bunch of clinics), Stanford University Press, and all of the research administration needed to manage the (many) grants Stanford gets.
These are admin-intensive things: federal contracting involves lots of paperwork, healthcare + insurance is a nightmare too. Plus, many of these involve staff that aren’t students (nurses at the hospital, scientists at SLAC, etc), all of whom still need “normal” admin things like parking, HR, and payroll, so the per-student denominator is a bit misleading.
And they have their own police force, own thousand of houses, and all the infra too (including streets, roads, sewers, etc).
Stanford is immensely rich, just considering their land holdings alone...