Not so, at least not in '06 and '07 when I was there. In the case I'm talking about, I personally know the guy who did the electrical work. HCNs did things like take out trash, clean latrines, wash dishes etc. They also served as translators. I never knew of any HCN doing anything like electrical, plumbing, water treatment, carpentry, food prep, or any other job requiring any kind of specialization. Just general labor and translation.
Military QA/QC did not maintain "direct" supervision over much of anything. They came around and looked things over once in a while, maybe once a month, if that.
When I was deployed to Iraq from 2005-7 (yes, I got the jumbo deployment) expats generally supervised work down by third country nationals. Most of the third country nationals were from Pakistan and India. Towards the end of my deployment in 2007, local Iraqi firms starting to take over a considerable portion of the work, especially road maintenance and construction of concrete blast barriers. The only supervision of the local Iraqi firms that I observed came from soldiers escorting the workers.
Things change. I left Bagram in ‘04.
Back then, all new construction was done by HCN’s. KBR Village was constructed by HCN’s. KBR was strictly O&M.