I've known some people who did contract work for the DoD like how you describe. They reported to DoD employees and were otherwise indistinguishable from actual

I've known some people who did contract work for the DoD like how you describe. They reported to DoD employees and were otherwise indistinguishable from actual DoD employes. However, there was some company that did their W2s, and took a cut almost as large as their salaries.