Now, I have never personally seen the definition of brain dead used to include someone who still had brain wave function(A layman might say so, but a doctor knows the difference between someone being really brain dead, and someone just being in an irreversible coma)...an irreversible coma would not necessarily be the same thing as brain death...I have taken care of people in irreversible comas, or in vegetative states...no doctor would ever call them brain dead...
Usually to be declared 'brain dead', there must be complete cessation of brain wave function(even minimal brain wave function indicates life)...unless you are saying that people with minimal brain wave function are being used as organ donors, which would of course be wrong...
But people who really are brain dead, can be placed on a ventilator, and the ventilator will keep their heart beating...the ventilator does what the dead brain can no longer do...now, ventiltors serve a purpose for those who need assistance breathing...but if someone is actually brain dead, the ventilator does nothing more than keep a heart beating in a person who is actually 'dead'...
If someones brain is completely non-functioning,(no brain wave activity), then that person is dead...the ventilator used to keep their heart beating, will never ever cause them to become 'alive'...
Someone who is truly brain dead(absolutely no brain wave activity, ever), is dead...nothing anyone does will ever make them live again...someone who has minimal brain wave activity, is not dead and should not be called dead...
But once someone is brain dead, harvesting their organs will not make them any more dead...they were already dead...harvesting the organs of someone who still has brain function would be murder...harvesting the organs of someone who is really 'brain dead', would not be murder...
I, too, used to think that logic prevailed in the medical community. Your logic is sound. What is faulty is the belief that your logic is not routinely violated.