If you're a US citizen, the US government already knows enough about you from just your regular stream of activity that makes its way to them—your taxes, any times you've been arrested, etc. So—even disregarding stuff like Prism—they already have a baseline estimate for how trustworthy you are, without needing to do a background check. (Also, they can rely on other partial background checks you've passed in the past, if they have access to them. If you've ever worked with children, or gotten a NEXUS card, they already have all the information they need to determine whether you can work a government job.)
The same cannot be said of foreign citizens (even ones who are permanent residents); to the government's eyes, they're "opaque"—and even background checks run on them would only turn up what their homeland wants the US to turn up. (A background check that could turn up more, wouldn't really be a "background check" any more, but rather espionage, since they'd need to bypass the "public API" of the other government.)
