It's one of those questions that is ultimately about the greater good. Yes, you would be betraying the trust of someone who had been alive, but since they are no longer alive they won't know and it will do them no harm. On the other side of the coin, you could help someone who is still alive to stay alive for longer. By refusing an organ you would not exactly be doing harm, but would you be sanctioning harm already in existence that your decision could assist and possibly correct?
If the person who was against organ donation was someone close to me, I might well try to persuade them while they were alive. I might even tell them that I didn't want to be held by such a wish once they were dead. In which case they could get some sort of legal injunction against me, I suppose.
That wouldn't bother me because I would have done my best to make sure what I felt was right happen. If it was prevented from happening by someone else, I might be sorry for it, but I wouldn't be responsible for any wrong (or harm, or lack of help to someone else) that then ensued.
So, unless forbidden by law, I think I would override such a wish.
This does not mean I would necessarily override other wishes. It would depend on the circumstances each time. So I guess I'm saying that I don't think a dead person's wishes need always be followed, and especially not when someone stands to gain from those wishes being ignored.