The author fell for the dumbest D&D misconception ever.
Because see, everyone, a fucking nat20 is not an autosuccess on a skill check, otherwise a lv1 player would say "I jump to the moon" and roll Athletics long enough... And one in 20 jumps would land him on the moon. Neither is a nat1 a skill check autofail.
And that use of Persuasion is literally impossible as per rules as written. What a shitty GM.
I think saying the author "fell for it" isn't really fair. If anything, I think the author knows how bullshit that interpretation of the rules is, and this whole story has been about different genres trying to out-bullshit the other.
All the factions have been exploiting the rules of their game systems so far that we've seen in some way. The RPG forced an outcome due to a scripted cutscene. The isekai protagonist instantly defeated an enemy that shouldn't have been possible to do so, though I can't be sure if that's just because he's "overpowered" by definition or some other reason. And even Takuto has been exploiting his own rules by making guns for almost free just because of a technicality, and is now exploiting it further due to his inability to die (presumably linked to being an RTS player avatar).
Also remember that Atou did actually manage to break the brainwashing for a moment, and Erakino commented how it must have been a guaranteed success that didn't even need to be rolled for - so we can assume that some part of the rules of the tabletop game defines the limits of the results of a nat 20, but that they're using the most generous interpretation possible.