True, but with some very legal caveats. If you suspect that the "brain death" decision may be abused for you, or your family; simply ask that they NOT harvest the organs after death. In essence, as a legal representative of yourself, your spouse, or children, remove them from the organ donor program. The hospital cannot steal whatever they want, from a body. These organs must be collected very soon after death - otherwise, they too die and are unusable.
They are harvested before death from a person whose bodily functions have not yet ceased, without anesthesia, and I have a moral problem with it.
There are probably a few others but the only viable body parts I know of that can be taken some time after death are corneas.