5e doesn't say what you describe. There's a small section in the DMG that vaguely says the DM might ignore the dice sometimes, but hardly a full-throated embrace of fudging or DM supremacy.Especially in a system that explicitly tells the players that the DM can change the rules and tells the DM over and over and over that the rules aren't in charge, the DM is in charge. 5e(and every other edition of D&D) assumes that the DM can override the rules when he feels it is appropriate.
There's nothing 'telling the players' this and there's no 'over and over and over'.