No, the assumption is that when the private operator screws up he will get fired and replaced.
Thus he has an incentive to hide the mistake for as long as possible. At the same time he has an incentive to cut as many corners as possible to minimize costs, so he can make the lowest offer. You can counter these by making him unfirable for anything short of intentional sabotage, and by providing the contract at profit + costs, but then you have lost all the supposed benefits of privatization and are actually paying more - those profits.
Apparently you are unaware of this basic economic principle which those who push privatization take as a basic assumption.
Economics has nothing to do with either proposing or opposing privatization, it's all about ideology.