The action of being in the country might be unlawful, but the person himself is not unlawful. The use of "undocumented" instead of any other word not a "tactic to downplay the issue", instead it express the lack of legal residence status is due to not been able to obtain documents to correct its residence status
If we transfer the characteristic of the action to be a characteristic of the person then if you have drive above the speed limit, you are an illegal driver; and so on
But don't worry, I am pretty sure ICE was waiting for him outside the court