If you actually go to the source behind that figure (http://facts.stanford.edu/administration/) and scroll down, you'll find that it actually doesn't refer to the number of administrators--far from it--but rather just the total number of non-academic (i.e., not faculty) staff. Indeed, that figure includes service and maintenance staff, clerical workers, and employees of SLAC, in addition to "managerial and professional" staff, which includes research technicians, of which there are surely hundreds in the SOM alone, librarians, biostatisticians, accountants, lawyers, engineers, grants specialists, programmers, and yes, of course, administrators, among many other titles, but it's just downright wrong to say that Stanford has 12,508 administrators.
At my university the graduate students (in the engineering college, at least) were frequently research assistants. In that case you would probably be counted as an employee of the university.
That data point could change the student-employee ratio from 1:1 to 2:1
