But we're not god.
In a single-player CRPG, absolutely we are.
Our characters are not, but we as players absolutely are.
Our perspective is fundamentally anchored, and our ability to define the world is clearly limited.
We're not omnipotent, but that doesn't make us powerless.
Everything not impossible is possible.
As I understand P&P (never played it myself) this would be a good analogy to it - you can't just imagine away what other players say, or how the DM defines the environment or the encounters. You just control your own character, and your perspective is limited to what we IRL would be limited to - i.e., sight etc. You can decide how your character interpret stuff, and to some degree you have control over what that character expresses - but in a cRPG you have to account for the medium, which is why options are heavily, heavily constrained and we need e.g., tone indicators - but that's it. You don't get to control the other side of the conversation.
P&P is a multiplayer game, and thus different-in-kind. The need to accommodate actual human conciousness other than your own changes the game considerably.
That said, the GM can do exactly what you describe. Like in a single-player CRPG, there is no objective reality. The GM can change previously established facts about the game world at his whim (ideally before the players learn of the original state). From the players' perspective, this manifests exactly like Schrödinger's Lore, where no proposition about the world is true or false until discovered by the players (or better yet, the players' characters).
An NPC might have no backstory at all, or he might have a detailed backstory the GM wrote but you never learn, or you might inquire after the NPC's backstory and the GM rewrites it on the fly, even though he had preciously written a different one.
There are many roles to be filled by the participants in a tabletop RPG. Typically, each participant (save one) will act as player, controlling a single character. The final participant will act as referee (the GM or DM, as you prefer). When translating this to a single-player CRPG, there's no reason why the one player needs to fill the role of just one of the tabletop players, with the other players and GM being controlled by the computer. Instead, the player could fill all of the player roles simultaneously, controlling multiple characters. Or, he could fill the GM role, with the computer filling the player roles. Or he could fill one (or more) player role and the GM role, leaving only the balance of the player roles to be filled by the computer.
I lean toward this last arrangement. The actual CRPG then takes the form of a detailed sourcebook, like a published module (Tomb of Horrors, or the Temple of Elemental Evil) or a boxed set (Greyhawk Wars, or the Rod of Seven Parts).