The rule is an extension of a precedent set by WoTC themselves
The lead rules designer of 5e, Jeremy Crawford, has1 the power to make official rulings, and frequently does so on Twitter, and in the Sage Advice column on the official D&D site.
It's common for him to answer questions with some variation of "if a feature was meant to work that way, it would say so." He has even explicitly stated:
Beware of claims that a rule does something mentioned nowhere in that rule or elsewhere in the core books. There aren't secret rules. (source)
Using this principle, he has made rulings such as:
The Dual Wielder feat doesn't include the benefit of the Two-Weapon Fighting feature. It would say so if it did.
(source)
or
If the grease spell created a flammable substance, the spell would say so. It doesn't say so. (source)
From this, we can derive that barring some explicit clarification from Sage Advice, JC himself, an official errata, or a more specific rule mentioned somewhere else in the game's official material, features in the game are intended to only do what they say. Though, of course, the DM is permitted to make their own rulings and allow spells and effects to do things not directly stated in their description as they see fit.
1 While this status was subsequently backed away from (official rulings only now apply to the Sage Advice Compendium as posted by WoTC, not the tweets from J Crawford), it was true that his ruling was authoritative when this question was asked, and answered; that change in state does not change the overall point.
Don't accent the rules — describe what happens in the world
Decide what you’re trying to accomplish first, then consult the rules to help you do it. As a DM, you help guide the narrative and bring the world of the adventure to life. From this perspective, the rules are not directions, but a tool:
The rules serve you, not vice versa. (DMG page 235)
When you make a ruling, in order to prevent arguing, ensure you provide a plausible in-world explanation for players (e.g. "you can't put this trinket in your mouth, because you have no time", not "because the rules say so").
Considering the provided example — casting the Darkness spell on an item and hiding this item in a mouth is actually a clever idea. But your player's intent wasn't to invent a smart tactical move, but to "trick" the game world by abusing the turns mechanic.
But you can't trick the world. Unlike a computer game, the game world in D&D is not the mechanics, that's why DM is needed in the first place. Distinguish between what happens in world (what character see) and what mechanics do you, the DM, use for resolving the situation. Explain, why sitting in complete darkness is a bad idea:
— I could cast darkness on the lip piercings.
— It will effectively render you blind in the middle of the combat, are you sure you're doing it?
— But I can cover the darkness when my turn starts, can't I?
— Not exactly. We (players) use 6-second round mechanics to organize the combat pace, but for your characters there are no "turns". They are just fighting the bad guy and all act simultaneously. You can dismiss the darkness when you hear something, I will use the Ready action to resolve it. Do you do this?
More info - How does time pass in combat?
Best Answer
July 9, 2008
This is when the Quick Primer for Old School Gaming by Matthew Finch was published online. It's the first example I can find of the exact phrasing and seems to be the original source.
This isn't a 5e thing. In fact, 4e was only a nascent edition at this point, being first released in December 2007. The primer itself is about playing 0e.
To quote:
Given this, I can't help but think that the sentiment is much older, but worded less memorably.