Oh, I know I shouldn't feed the troll but...
1: That little part near the end there was what I've dubbed through the years as "homebrew disclaimer". If you have been around D&D products long enough you will know that they like to remind people that it's okay to add things to your home games. Some people feel like they need to stick with the cannon and sometimes they liked to remind us that it is okay to use whatever you want. Unfortunately this is not cannon. It was also a small form of advertising of the other D&D worlds. They were letting people know that using more than one world is okay.
Quoting Ed Greenwood's introduction 1987 dark grey boxed set, word-for-word:
The "Forgotten Realms" derive their name from the fictitious fact upon which play in my campaign is based: that a multiverse exists, of countless parallel co-existing Prime Material Planes (including the world presented herein, our own modern "Earth", and any other fantasy settings a DM may wish to incorporate in play), all related to the Known Planes of Existance presented in the AD&D system.
It seems pretty damn clear that Ed was happy setting the Realms in the existing D&D cosmology and was pro-multiverse.
2: Co-existing primes are still prime material planes that exist with in the Forgotten Realms sphere. Oerth (Greyhawk) doesn't exist with in the same sphere is not an alternate prime material plane. Something came up years ago about this when a question was asked to Ed Greenwood about Lolth. They asked if the Lolth on Oerth had any connection with the Lolth in Forgotten Realms. The response to that was no. It was said they are completely separate entities that had nothing to do with each other. Now if these worlds co-existed why wouldn't there be one Lolth who has extended her power across these alternate worlds?
Citation please
3: I have all FR products from 1st, 2nd, 3rd, and 4th edition. None of the official products mention anything about Oerth, Krynn, Darksun, or Mystara. If these worlds co-existed in cannon then we would see some evidence in 30+ years of gaming material.
Then you would have 1993's
Code of the Harpers, which mentions Oerth, and is written by one Ed of the Green Wood.
Plus there are a couple crossover adventures.
Castle Spulzeer, from 1997 starts in the Realms and then continues in Ravenloft in
The Forgotten Terror. And
For Duty & Deity crosses over with
Tales from the Infinite Staircase.
This is without getting into Spelljammer which pretty explicitly mentions being able to travel between the Realms and Oerth and Krynn.
The only thing we have is an older Dragon mag article about Elminster having a get together with Mord and Dalamar and that wasn't even written by Ed Greenwood.
The first of these would be
Magic in the evening, written in Dragon #185 from 1992 by... Ed Greenwood.
You'll find others in 188, 196, 200, 211, 238, 242, and 246. To name a few. All canon, like everything else Ed has written for the Realms.
4: When the Forgotten Realms was created there was no such things as Oerth or any other published D&D world, D&D wasn't even invented yet.
Nope. Neither did Drizzt. But it'd be silly to argue he isn't part of the Realms.
The Realms, as published by TSR, is not the same Realms as that Ed Greenwood used as a setting for his stories. Or likely even uses as the setting for his homegames. It's a variation/ derivative.
You are basing your argument off of a homebrew disclaimer that is found in many books where it just reminds you that it's okay to add stuff outside the cannon into your home games. It sounds a little like you might be a bit of a Wiz fan and are trying to justify their crossover strategy by making it seem like the Realms has always been built around these other published D&D worlds when it hasn't.
"Wiz fan"?? "Their crossover strategy"??
The D&D multiverse is a TSR thing that predates the founding of Wizards of the Coast.