What do you do when your project changes dramatically during execution and it becomes obvious that you need to change the objective?
Jim Lovell, 3/4 of the way to the moon
Haha! I was watching Apollo 13 Saturday night also. Lots of great Project Management stories in there. I'll have to do an analysis of this movie one day. But your question allows me to address one aspect of the case.
I use NASA when I describe the need for every project to have an official objective that everyone agrees to. I don't know the objective of Apollo 13 project but the objective of the Apollo program was: 'To achieve a manned lunar landing and safe return of the astronaut by the end of 1970 within a cost of $40 Billion.' From that program objective, I can only assume that a major part of the Apollo 13 project objective concerned landing on the moon and returning the astronauts safely.
When the explosion occured and the spacecraft started losing oxygen, the powers that be had to make a decision. What do we do with the project at this point? They had a two-part objective. But with that significant an oxygen loss, which could only be stopped by shutting down two fuel cells, they could only accomplish one of the two parts: Land on the moon or return the astronauts safely.
Who gets to make that decision?
Not the project manager, not the team. We're talking about the steering committee at this point. The same people who signed off on the project in the first place. The steering committee or whoever provided the budget for this project in the first place. I don't think that person showed up in the movie. The movie shows flight command making that decision.
I'm sure that the decision was ratified at the right level, we all knew that they had to get the crew back to earth. When it's an emergency, the Project Manager or the man on the spot, (that's you, Jim,) can also make the right decision but get approval as soon as the emergency is over.