But you would not hide this, as you've said. You would instead say something like, "Oh, I shouldn't have asked for a roll, that just happens."
Regardless, what you're saying here is that you made a mistake. I don't see how "very rarely, I make a mistake and thus have to do a thing" makes any comment at all on whether the rules are binding. Instead, it seems to me that what this says is "the GM really should follow the rules, and when they flub up and fail to do so, it's on them to fix the problem".
It's harder to encounter a corner case with rolling where the rule would need to be changed/ignored on the fly. While corner cases are rare individually, there are enough rules in 5e that some corner case popping up is not all that uncommon.
When a corner case pops up where a rule should not apply because it doesn't make sense to apply it as written, the DM can and should make a ruling on the spot changing the rule. Now the players know that when/if that corner case ever pops up again, the rule is going to be Y instead of X.
This is why the 5e DMG says things like...
"And as a referee, the DM interprets the rules and decides when to abide by them and when to change them."
"The D&D rules help you and the other players have a good time, but the rules aren't in charge. You're the DM, and you are in charge of the game."
"The rules don't account for every possible situation that might arise during a typical D&D session."
"The rules serve you, not vice versa."
"Remember that dice don't run your game-you do. Dice are like rules. They're tools to help keep the action moving."
"AS THE DUNGEON MASTER, YOU AREN'T LIMITED by the rules in the Player 's Handbook, the guidelines in this book, or the selection of monsters in the Monster Manual."
Most of the time the DM should alter rules in advance and inform the players of changes to the rules that are made, not spring them on the players during game play. However, sometimes that pesky corner case pops up unexpectedly and the DM has to make that ruling right then and there.
The players will know the difference between the DM adding Low Light Vision back into the game and giving that to elves instead of Darkvision, a rule done in advance and told to them. And the DM pointing out during game play that X rule doesn't make sense for Y corner case situation, and so Z ruling will be in place for that corner case now and in the future.