But that's not just it. Whether you realize it or not, you're adding connotation. Your word choice suggests a certain amount of moralizing about playstyle.
Is the mechanic slightly metagame? Sure, insofar as it is a chance of the players to choose some of the narrative direction through something other than the task resolution mechanics of the game. But you could have said, "That rule is a bit to metagame for my tastes". Instead, you said, "oops rule" which has the connotation of being the thing you do when you weren't careful enough to avoid a mistake. An "oops rule" is something you use to cover when you're sloppy.
But, this is baked into the system. It is something the GM and player can rely on, as much as you can rely on hit points in D&D (and in much the same manner, at that, from a player perspective). There's nothing sloppy about it.
You're free to not like it, and even say so. You're free to not use it. But the connotations you are bringing to the discussion are inaccurate, and unfair.
For me, the connotations are totally accurate and totally fair.
The game system has a hole. In that hole, PCs can easily die. So, the game system put in an "oops" rule to prevent that from happening. The rule is total metarule, not in character rule. The vast majority of other game systems do not have this rule because they do not have the hole. The PCs are not changing the outcome of what should happen to something else, the players are. They are doing it within the rules, but that does not make the rule any less of an "oops" rule.
The results of the players using this rule affect a totally different entity (i.e. an organization) that although the PCs are part of, the DM now has to come up with a narrative way as to how in this particular case, moving the damage to the organization adversely affects it. It also differs from 5E "oops" rules which tend to just affect one PC or a small group of PCs.
5E has "oops" rules. The Halfling Lucky rule. The Lucky feat. Many of the reaction abilities and spells. These are rules that change the outcome of the normal task resolution mechanics of the game and they typically do it when the PC is at a detriment. Not quite as sure fire as the rule you mentioned (where you implied that the players make the decision and things just work out in the short term), but still "oops" rules.
The rule you mentioned has differences in that it can more easily affect multiple PCs simultaneously, it directly affects outside entities, it is required or the game can suddenly end, and the implication is that it always works and any player can use it. But it also has similarities in that it is a limited resource, it comes into play when a PC or PCs are at a detriment, and is part of the normal rules.
So yes, there are some pretty significant style differences that you seem to be glossing over. But I use the same "oops" terminology for some 5E rules as well, but they are not quite as "OOPS" protecting as this rule is.