I think you totally misunderstood what "game-mechanics design" is if you're thinking that Valve would be the one to do game-mechanical prototyping.

The creators of Narbacular Drop — if their goal had been to make a AAA game ala Portal† — would be the people who should have sat down and worked things out with legos and pipecleaners.

† (Which it wasn't — they built a game basically as a class project, a proof-of-concept; they didn't care about making a fun game per se; about discovering a novel challenge-space wide enough to build out a set of scenarios deep enough that they could keep a player's attention for a few hours and make it seem worth $60 or whatever. They built levels just to prove that the physics worked.)

This is because, in order to actually implement Narbacular Drop, the creators had to sit down and write an entire custom game engine from scratch, to make their game possible.

(A.k.a. the "Sketcher Engine." The Source engine wasn't public in 2005! And no existing publicly-available game engine in 2005 had support for sub-rendering of secondary view frustums onto textures to be included in a primary view frustum; nor for "proxy" physics objects representing an object being in multiple places at once [Chell standing half-way through a portal] where both have collision but only with things on the same "side of the portal" they're in, so that they don't collide with their own alternate self. Oh, and even if they did — DigiPen doesn't let people in their game-design program use external black-box game engines in class projects. You always have to implement the game engine yourself.)

Insofar as Narbacular Drop is considered a separate game, though, Portal really doesn't have any novel game mechanics; it's entirely derivative (though it does combine the "3D traversal with portals" mechanics of Drop with more traditional 3D-puzzle-platformer and graphic-adventure game mechanics, to produce a novel — and very polished — game.)

As such, Valve didn't need to do any mechanical prototyping. Narbacular Drop was the proof-of-concept of the mechanics. Portal was a simple port of those mechanics into Valve's engine. You don't re-do mechanical ideation just to steal another game's mechanics. You already played the original; you already know the mechanics are good.

(I would note that Valve have never been one to innovate in game mechanics. Half-Life, for example, is an innovative game, but it's one built by taking a bunch of physics-toy interactions (e.g. exploding barrels) that were seen in older titles, and making a game entirely out of those interactions, where you're supposed to use them to kill enemies.)

> is this true? from my recollection, this all began in the wake of the release of the initial announcement trailer for the original Portal back in 2006.

The "Now You're Thinking With Portals" meme originated in 2007, yes.

But people have been trolling each-other with images of impossible 2D top-down puzzles saying something like "find the exit" — where one common "solution" is to draw a wormhole that takes you right to the exit — for years before that. And then parodying those, by drawing complex 2D-side-on platform-puzzler levels, where the player-avatar's route takes them through walls and narrow gaps.

This genre of meme-image doesn't really have a name of its own, which makes it hard to search. After portal, it evolved into the "Get The Cake" meme. But I can assure you that it existed before there was a cake involved!