The USPS is most certainly a government organization. It's mentioned in the Constitution. (that's the first clue). Where people get confused is that it's called

The USPS is most certainly a government organization. It's mentioned in the Constitution. (that's the first clue). Where people get confused is that it's called a "independent agency" which simply means it doesn't fall under a Cabinet-level post. It is, however, controlled by Presidential appointees (that't the other clue it's part of the government).