I'm not aware that a medical procedure is opt-out, I always assumed it was voluntary.

Unlike this state mandated organ seizure, if you haven't heard the news and opt-out of yet another thing.

There are about a million other things done to dead bodies that will kill a mistakenly-identified-as-dead person as stone dead as removing an organ, so organ donation specifically doesn't really have a special status here outside of it being potentially the first item on the long checklist.

Emergency procedures are often done without consent. Because patients are often unconscious and cannot give consent. Just like in your story.