I don't see how Augustus could've been wrong? Maybe he didn't have to be an arrogant ass, and could've just calmly explained the matter. But considering the critical time, he did save the rest of the crew and the system probably.
Whereas the captain, though he had noble intention lost a crew member, and gave no precise commands when the event horizon was approaching. There was no need to kill Augustus in the end. Just a pathetic show of power.
Absolutely, Augustus wasn't a ass but the savior of humanity.
The story for me made very clear how the captain was a man from the past, still very attached to old beliefs and not accepting the future knocking on the door, being a captain only for how the system works and not really because he was the right man for the job.
His care for the crew was correct but he wasn't thinking, or wasn't able to compute on a larger scale.
Augustus and his comrade simply couldn't explain everything when every second was important.
And the captain killing Augustus at the end was simply revenge for being abandoned, something that had to be done, probably 5 seconds more attached to the ship and they wouldn't have been able to escape in time.
Augustus saved everyone he could, he wasn't even a ass, just cold, and seems like this new generation wasn't much expressive, not a reason to kill them, he didn't abandon the captain because of hostility but logical thinking, absolutely undeserved death.
If the system works the captain will be sent to prison for homicide towards a unarmed subordinate that had just saved the crew and the solar system, possibly executed, if the system doesn't work being fired/dismissed with dishonor would be the minimum sentence.
Check even how the captain behaviour when recounting the events, sure of himself, of being untouchable or having done the right thing, not a word commenting his own mistake.