Most non-university non-industry non-government research institutes in the US (eg. Salk Institute, J. Craig Venter Institute, Sanford Burnham Prebys) rely on their researchers applying and getting grants from the NIH and NSF just as university scientists do. And their overhead costs are generally even higher than universities because they have no other source of income other than grants (I used to be faculty at JCVI). HHMI is unusual in that it is funded by a rich person's estate and doesn't need this.