Personally I don't think you should get involved. I think it's up to the person involved to fight her own battle, iykwim.
Not to mention if I was the boss of somewhere I wouldn't like to be told how to run something by my staff after I've already made the choice... and if I was male management i'd probably like it even less ><;
Yeah, I agree with Helle. I think it is inappropriate for you to be involved, particularly since you are not involved in the hiring process of that department. If the person is not happy with the decision for not re-hiring then they should seek the appropriate channels for either reconsideration or a complaint.