My interpretation of the text in the books, where the DM narrates the results, is that they didn't tell the DM to honor the results of any checks or other die rolls because they didn't think they needed to. I mean, in principle, if the DM doesn't want a check to be passable they can skip the roll.I think it's possible to bring a shared expectation that the DM should make their rulings firmly with only the fiction in mind (as was the original expectation in older versions of the game). I'm not seeing that as a general expectation in the DMG what with all the lead storyteller language it seems enamored with.
I do think the vast majority of DMs try to respect the players' dice rolls, but more in a improv storyteller fashion where you are still skewing results in certain directions. I know you do not run the game that way, but I have encountered it all over the place. I think it's quite compatible with the DMG.
(And thanks for the vote of ... trust or confidence. I genuinely appreciate that.