I agree with this. This GM may well have been unfair. But that's not relevant to the question of whether or not the paladin did the right thing. It is relevant to the question of whether or not I would want to play (a paladin? at all?) in this GM's game.
Okay, I went a bit far back to pull this quote, but I think it goes to part of the issue that's being discussed here in isolate or in different contexts. There's the thinking of the paladin's oath and nature that divorced from the fact that the paladin class is part of a game. I agree with a lot of what's been said about the nature of such a divine warrior in fiction in general, and in archetype. However, I think that such thinking is in error when analyzing what's happened in a game. Even assuming a better scenario than what's presented, the consideration of how a character's archetype is realize in a specific game given the mechanics will vary a great deal. There's the fact that you have imperfect communication, or small (or large) differences in underlying assumptions. Heck, this thread alone is a good indicator of how honest engagement on the topic can result in some small but intractable difference of opinion in what a paladin archetype is.
So, I think that the game being played is a critical part of interpreting the ability and fidelity of the archetype. When we see the holy warrior, the knight, the super-solider trope, it's almost always best rendered in straight fiction where the toils and troubles faced are constrained to allow the trope to shine. It also works well in RPGs that have mechanics that strongly enable player input to the fiction, or that adjudicate the game according to the player proposed fictions. PbtA games do this, as does BW. These games enable the trope by directly making the game about the trope (at least to a large degree), and functionally enable exploring the trope in a way that rarely levels character ending consequences, or does so after a clearly engaged spiral of play towards that ending. D&D does none of these things. The nature of the DM-directed play in D&D means that there's much more room for DM/player disagreements about the trope to hide until character ending consequences are already being employed. Further, the nature of D&D says that the DM should arbitrate the player's play against the trope and level character ending consequences for whatever the DM determines to be sufficient divergence from the trope (and, yes, I'm calling pushing oathbreaker of removal of class abilities character ending -- it's not the same character anymore and may not be something the player has any interest in playing). This makes evaluation of the trope a bit different, and, indeed, I believe it requires alteration of the trope as it exists in pure fiction. If the trope requires sacrifice for it's tenets, then it's going to run afoul of many of D&D's other tropes, like the DM's interpretation is the correct one (woe to a player that doesn't guess right), the DM establishes both the scenario and many options and the outcomes of said (again, woe to the player that doesn't guess right), and there's a heavy bias towards lethal outcomes in combat. Given that the nature of the trope in question literally begs to be tested, these two D&D tropes will always cause problems in attempting to realize a more full version of the trope. It becomes a suicide mission, not in service of the trope, but because the nature of the game will eventually cause conflict with the other tropes of the game.
This requires either modification and softening of the trope, which the sidebar in the PHB does, to some extent, or a better negotiation of outcomes between the player and DM, which is somewhat outside the usual guidance for running D&D games.
I'm seeing a lot of evaluation going on the is either focusing on how the trope plays in fiction, which is a bad fit, or how it plays in games that treat it better than D&D does, which, again, is a bad fit. I also see modifying the scenario to be more engaged with the play in a more open manner, which is always good advice, but not necessarily helpful with the immediate case. Counterfactuals rarely illuminate a situation. I think all of these lines, while interesting, don't really address the situation in the OP. Nor do they really address how the trope plays in 5e. Evaluation of the trope in other situations or methods of storytelling is good, and I agree with a lot of what's been said about the nature of the trope in these evaluations, I just don't see much utility in them in regards to how the trope plays in 5e in any healthy way. Applying those considerations to 5e play ends in the exact scenario presented in the OP -- where the DM may have imperfectly run a scene but now the character representing the trope must be held to it, regardless. This isn't a healthy game.
To play the trope in 5e, there needs to be either a relaxing of trope requirements on the player side -- ie, making transgression harder and more pragmatic in consideration, or the DM must take great care in how they engage the trope in play. This latter is difficult because it's trivially easy to create normal D&D play scenarios that directly implicate "stupid" play under the trope. I scare quoted stupid because I mean stupid in the sense of actively going against other existing D&D tropes that will result in poor outcomes for the character just by the nature of D&D.