The 1e books say many contradictory things. Fortunately, I never read that marketing pitch. I probably would have never played D&D if people were trying to push that ethnocentric misrepresentation of other cultures on me.
Anyway, I only consider the "core three books" to be 1e core.
Young me was handed that book and told it was just an example of how gods worked in the game- I think most DM's had their own gods back in that era, and Dragon would crank out a pantheon here and there as well. A friend of mine swore by his Cleric of Rhiannon (with the strange power to turn animals). It never occurred to me that appropriation of other culture's mythos was even wrong, back then.
And yes, I'm aware, Gary's hyperbole was usually aimed right at getting people to buy his company's books and not go on to make their own competing product. But a whole generation of gamers took what he said as gospel- I know I've met my fair share of antagonistic DM's who would point at his words saying "this is how we are meant to run the game"!
Even if, like any religious text, the D&D bible can be used to prove or disprove any argument.
What, exactly, the relationship between gods and psionics is, and what it means to be a deity of psionics is still left very mysterious and murky. So far, we have seen that psionics can be-
Wild talents that some powerful minds possess.
A system of mental powers that can affect reality, that many people can learn to develop.
A system of magic with a different source than arcane or divine, and not subject to the whims of the Gods of Magic.
Spell-like abilities possessed by some creatures and races (even up to 5e, with races such as the Githzerai).
Powers derived from the mysterious and eldritch Far Realm, and the aberrations who trace their origins to that place (or other, native aberrations, such as the Aboleths).
Depending on the era, these abilities are more or less magical, and can interact with magic in strange ways or not at all. If one were to look at the campaign worlds and assume that everything that happened in those worlds throughout the decades is canon, despite these differing rules, we can see that psionics is in a state of flux. It changes, and whatever form it takes now may or may not bear any similarities to the form it takes in the future...or the past.
In Greyhawk, it is said that Illithids brought the knowledge of psionics to that world with them, when they crashed in a spaceship (spelljammer?) on Oerth long ago.
But it is also known that the Illithids have their origins not in the past, but the future. I'd like to postulate the theory that psionics are cyclical in nature- ancient psionics will eventually evolve to become the same as advanced psionics in some future time, and the time loop will start all over again.
So there's room for
all interpretations of psionic powers, and there's no reason that multiple such iterations could exist simultaneously. Because Illithids aren't the only source of these powers, just
a source.
The Aboleths have existed, so they claim, since before even the gods, after all. Perhaps it was psionics, not magic as we know it, that created the universe? Perhaps this was the First Power, that existed long before arcane energies were ever tapped by the protodrakes and their descendants, the Dragons?
You can do a lot with this lore, and a lot with it's myriad interpretations. Or nothing at all, and the game will still go on.