Earlier quoted context omitted.
Suitable candidates will be forwarded to our government contracting partners who will interview, hire, and place on our team. It is not government hiring so no need for listing on USAJobs
If it's not government hiring how is it legal to require citizenship?
Having the right to work in the US doesn't entitle you to a job. And there are plenty of reasons government institutions would want to disallow non-nationals a position. The whole point of citizenship is, after all, buying into the system; if you're not "in" your allegiances or potential recourse can always be argued to be limited. Dual-Citizens, such as myself, are in a similar boat for the same reasons (unless they opt to renounce foreign ties).