Generally, no, they don't bill at 0 savings. The rate is set on a per-institution basis. The rate setting process incorporates the documented economics of scale that that institution is achieving already. This is why schools have different rates; the more resources (instruments, facility use, computational, etc.) the university provides at no/low-cost to the researchers, the higher the rate.

If the rate wasn't set in this way, the overhead would be well above 100%, as it is in most labor-heavy businesses like consulting and law.