I'm won't claim that universities don't have a problem with adminstrative bloat, but looking at simple top-line numbers like number of non-teaching staff can easily be misleading.
I don't know about Brown specifically, but schools like MIT receive large amounts of federal funding to do research. Administrating that funding requires staffing (paperwork for proposals, contracting, accounting, invoicing, etc). MIT probably also has non-teaching research staff that are entirely grant-funded. I'd be surprised if undergrad tuition is paying for any of this.
I don't know about Brown specifically, but schools like MIT receive large amounts of federal funding to do research. Administrating that funding requires staffing (paperwork for proposals, contracting, accounting, invoicing, etc). MIT probably also has non-teaching research staff that are entirely grant-funded. I'd be surprised if undergrad tuition is paying for any of this.