DC poverty rates are about as bad as anywhere in the country and the income inequality is about as high as anywhere in the country. Not everyone who lives in DC works in government, or doesnt have a high paying government job.
It's skewed because so many of the government workers live in Alexandria or in MD/VA. I don't know what being a State would have to do with poverty levels since that is directly attributable to the Mayor's office and what they do or don't do. And DC has a Mayor.