I wouldn't claim that the government has the best of the best across the board. In some areas they do, like fighter pilots or criminal investigators. In others, they generally don't, like web application developers.
What I disagree with is the idea that the government is full of incompetent people, who just need to get fired for things to speed up and get better. It ignores the reality of how the government really works, and therefore who joins the government and why.