I've heard it said a lot of times in different fora and even in this stack as a generally accepted truth, but have the designers actually said this? Where?
The best I've found is in DMG 235:
Rules enable you and your players to have fun at the table. The rules serve you, not vice versa.
This article, titled "Philosophy Behind Rules and Rulings," is written by Jeremy Crawford, and contains the following: (emphasis added)
The DM is key. Many unexpected things can happen in a D&D campaign, and no set of rules could reasonably account for every contingency. If the rules tried to do so, the game would become unplayable. An alternative would be for the rules to severely limit what characters can do, which would be counter to the open-endedness of D&D. The direction we chose for the current edition was to lay a foundation of rules that a DM could build on, and we embraced the DM’s role as the bridge between the things the rules address and the things they don’t.
Page 4 of the DMG, in the Introduction page, says the following:
The Dungeon Master, DMG pg 4
[...] 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. [...] (emphasis not mine)
