I'm not an organ donor mostly because I think that some Doctor somewhere might give me up for dead since there are 3 people waiting for organs even though there is a slim chance I will live. That might not even be a bad decision on the part of the doctor (1 cripple vs 3 healthy people) but I don't want him to make that choice for me. If I'm alive and explained the situation for myself there is a good chance I would say "sure go for it, I'll be a brain dead cripple anyways" but I don't want that choice taken from me and given to some doctor with a few seconds to make a decision while he holds a knife over my still breathing body.
I don't know how it works elsewhere but here in sweden they don't check if you're a donor until they have already taken the decision to take you off the respirator ("killing" you either way).
So it's not like the surgeon walks into the ICU, scalpel in hand, looking for anyone too slow to run away.