No. Not exactly. You are clinically dead, brain dead when your organs are removed for transplantation to another in order to save the life of another, but your organs must be kept functioning , receive blood flow and oxygen via artificial life support long enough to keep those organs viable for transplantation.
This girl was breathing on her own. She was not on life support. Yet they took her organs.
If I'm breathing on my own, I don't want my organs taken like that. Her family didn't either.
Re the notion of 'brain dead' the definition varies by location.
Yes, exactly. If you're dead your organs are no good.
BTW in some states you must opt out of being an organ donor, otherwise you are considered to be agreeable.