The third American in space - and the first to orbit - had a problem.
John Glenn's Friendship 7 instruments indicated that his heat shield was loose. His spacecraft could be burned up during re-entry. Most ground controllers thought it was a false instrument reading.
There were two choices. Keep the retro rocket package in place, which could damage the heat shield, or jettison it and re-enter normally.
But who would make the decision? NASA had no established chain of command.
The outcome was:Keep the retro package in place, the heat shield wasn't loose and there was a false instrument reading, pilot landed the spacecraft safely.
Flight Director Chris Craft (the guy that brought Apollo 13 back) insisted that the Flight Director be the ultimate authority over flight decisions. Today, the President does not have the authority to overrule a decision of the Flight Director.
Failure is not an option, part 2 (YouTube)