First of all, so?Because there are very few (if any) rational reasons to not donate your organs once you are dead.
Second,
According the OP, there are rare occasions where people have their organs without complete evidence they are actually brain dead. He is afraid of that.
It's maybe not probable or likely, but few of us make every single life decision based on logic. In this instance, his (perhaps illogical) fear outweighs the mathematics.
I can't imagine wanting to upset so bad, that I'd give a shit what he does with his heart after he dies. Might as well browbeat the dude into donating all his money to feeding starving children after he dies.
Not all of us can be heroes.
BTW, people on the fence should check this out:
http://www.mayoclinic.com/health/organ-donation/FL00077
The kicker with threads like these it leads to people spouting about how, "If I was in that situation, I'd take the pain and be happy knowing someone would live!"
C'mon man... we'll never know that's true.
It's like Paul F. Thompkins on the "I'd take a bullet for MY son!" speech.