You're excluding a very significant detail.
Under normal circumstances Cpt Brilliant would be sure to get the recommendation. I doubt there's anyone in this thread who would disagree.
This would be a case of the characters both falling off the same cliff. The high HP character would be likelier to survive.
However, in this particular scenario Cpt Brilliant commits a grievous act of HUBRIS. He goes to his teacher and tells him what a joke of a teacher he is and that the teacher should be thanking Cpt Brilliant for being his student. Guess who the teacher is going to recommend for Harvard? Cpt Brilliant sank his own ship.
In this case, the low hp character falls off a cliff, but the high hp character decides to do a swan dive off the cliff onto the rocks below to show up the low hp character. The low HP character is doing his utmost to survive, and the gods/luck may also intercede on his behalf. The high hp character is not doing anything to try to survive (as swan diving is a poor survival strategy when falling onto rocks) and has forsaken the favor of the gods/luck by acting out of hubris, (wrongly) certain that he can force their hand. At that point, IMO, the high HP character is as good as dead while the low HP character has a chance to survive.
I see nothing unfair or inconsistent about it. The DM should certainly warn the high hp player of the consequences so that they can reconsider, but that's an issue of gotcha DMing which isn't pertinent. It's not inconsistent, since if the low HP character swan dives off the cliff, his death is similarly assured.