That's a useless suggestion: people who need organ donations are generally not suitable to donate, and they know it long ahead of time.
Except in cases of injury, or where only one organ is the problem.
Well, one reason is a concern that doctors and hospitals might be less interested in saving you if that means potentially damaging donatable organs. There are many other reasons as well.
Considering that, far as I can tell anyway, virtually every medical organization on earth denies that happens, that seems an extremely unlikely and unreasonable concern. I would not be surprised if there were isolated incidents, but by that logic you should wear body armor in case someone stabs or shoots you. I think its much more reasonable to trust the opinions of major medical organizations than put stock in baseless fears pulled out the usual place.