The Defense Department CAN NOT GET INVOLVED IN POLITICS per its own rules. These rules include situations like those described in the above story. The military remembers the bad press it got during the Vietnam war for reprisals against hippies (Even though the hippies and traitors deserved it).
They aren’t suing the Pentagon, they’re suing the Administration via Gates. He has the political office that oversees the military forces, and is the correct place to go for resolution. Congress passed the laws; the Administration is responsible for enforcing them.