Personally I think the individual's decision should be final, because the way our system currently works, they would have had to actively decide to donate their organs and sign up for the organ donor register. Therefore by not allowing the donation to proceed they are directly going against their loved ones wishes.
I definietly agree that everyone should speak to their families about this decision. I think many families would not want to deliberately go against the decisions of their loved ones, however grief can be a powerful emotion with can potentially influence people's perceptions of a decision such as this. I would think that when families are asked to allow the donation to occur or not, they would not necessarily be thinking about the lives it could save, but about what they think is best for their family member, regardless of that person's decision. This does not mean I think they should be able to override their loved one's decision, however it may explain the surprising statistics.
This may be a separate issue, but I believe everyone should be placed on the organ donor register by default, with a simple process for people to remove themselves from the list, or even if everyone was somehow reminded when they turned 18 to think about their wishes. This is because I think many people would want to donate their organs but just never think about it. However this would complicate the families issue because it is harder to tell whether the person consciously did want to donate their organs, so the family might be more inclined to follow their own wishes. I don't know, but I just don't see a reason not to donate your organs if it will save lives (although I will still respect if other people decide not to).
Very interesting discussion. Thanks for raising this, I am very nearly 18 so it has reminded me to register as well.