There's a reason for this.
I've got a few friends flying for these companies. In addition, in my current AD job I do the C2 for a specific AOR that relies on them. They are all bound by the same issues and they are all basically interwoven. The govt. assigns a rep to the contractors flying in support of DoD/DoS. While perhaps not wholly responsible for the rules and requirements they are the primary quality assurance evaluators to the contracts. In my case, the issue was that I lacked 300 hours of 'like aircraft' time (twin turboprop). I have a TS, A&P and ATP + 2k in A-10s, but not-eligible due to this stipulation. This was with a close friend's direct rec to 'the' chief pilot. To that end, I read the chief pilot's response, and he sounded apologetic. My opinion...most of these positions are held by former Army FW guys and the 'like aircraft' deal is simply to protect a good thing.
In my case, still not sure what I want to do after retirement, but I would gladly do a few months in Dash 8s for a regional somewhere...even thought of Ameriflight...