This seems a very shallow conception of what it means to engage the fiction of the game.
In the same way that saying a hit on the attack roll necessitates physical contact within the narrative, I'm sure. Just because you
could manipulate the facts in order to support some outrageous deviation, that doesn't mean you
should, or that you're even playing the same sort of game after you do so. If you don't "engage the fiction" through role-playing, then you aren't playing a role-playing game, and any arguments you make from that deviant context is irrelevant.
I will illustrate with examples from my two 4e campaigns.
Probably not the best example, given the reputation of that edition. Fourth Edition marks the point where players have become
so paranoid about terrible DMs manipulating things behind-the-scenes in order to make their choices irrelevant, that the designers gave up on the idea of a logical or consistent world
entirely, in the name of making the numbers
so transparent that players would be able to call the DM out if they tried to cheat.
And as far as the integrity of GMs is concerned, they're pretty resilient. I'm not going to corrupt them, I don't think.
You have said nothing which has not been said before, so that places a limit on the amount of damage you can do. All GMs who manipulate facts behind-the-scenes
believe that they're making the game better, unless they're of the old-school variety who simply believe it's their
right to mess with the players. Either way, when players realize what's going on, it makes them distrust that GM; and if it keeps happening, across different games and GMs, then they learn to distrust all GMs by default; and then they quit the hobby entirely, because they've been burned by so many GMs (well-intentioned or otherwise) that it's not worth the effort to even find a game.