Supposedly (I can't find a reliable source), Neil Armstrong was once asked what he would have done with his final hours on the moon if the ascent engine had failed and they had been stranded. His response was that he'd have spent his final hours trying to fix the engine.

The point is that there's always something to try, even if it's improbable. Pilots are told to fly as far into the crash as possible, because it never helps to give up, and there might still be something you can do.

It's possible that they chose to say that because they thought there was no way to save the astronauts, but they definitely did not have to. And if that's really how it was, they definitely shouldn't have.