At that same time, though, I worked for a contractor that I do believe saved states money compared to doing things in-house. The work we did really required specialists. But no one state had enough of the work to keep one busy all year. So sharing a pool of people to do the work among many states meant there was room for both saving the states money and allowing some profit for the company.
The idea that you can just blanket assume that private industry is inherently more efficient than public works really needs to die. There doesn't seem to be any more evidence to support it than there is to support the idea that it's inherently less efficient. Life just isn't that simple. It's all case by case.