Shouldn't most scientists be getting their pay from universities, or the R&D departments of corporations? I mean, the CDC and NASA don't employ that many people

Shouldn't most scientists be getting their pay from universities, or the R&D departments of corporations? I mean, the CDC and NASA don't employ that many people in the grand scheme of things. You don't have to be an employee of CDC or NASA to get your pay via government funding. The university signs my paychecks, but the money comes from an NSF research grant to my co-advisor.