Well, to be specific-
Gygax repeatedly claimed (or allowed to be inferred) that he was the real creator of D&D. But ...
...the best case for this is Chainmail. As we now know, but Gygax never divulged, EGG ripped this off from a college student's rules for a Tolkien wargame in New England. But wait, it gets better! The only evidence that we truly have is that Jeff Perren (his co-author) read that material about the Tolkien wargame, so it is entirely possible that the idea for adding the "essential" Fantasy Supplement to Chainmail came from Perren.
Then, we also know that RPGs aren't a Gygax idea. We now know that they originated with Braunstein, and that Arneson took the idea (which was really basic at that point) and developed it. And that it was Arneson that developed the fantasy RPG that became D&D.
...and that he taught the game to EGG, who realized the commercial appeal it might have.
None of this diminishes the importance of EGG; without him, there wouldn't be D&D as we know it (duh), and who knows what would have happened with TTRPGs. After all, history showed us that Arneson was more interested in running fun games than developing a business, or even keeping a coherent rule set.
The genius of EGG (well, one of them) is that he was able to take from so many sources and put all of those disparate things into a rules that you could play. That is not a small feat. He could take a little Lieber, a little Tolkien, a little Vance, a little Howard, a little Lovecraft, a little Indian mythology, a little Norse mythology, and a WHOLE LOT OF OTHER PEOPLE'S WORK IN THE HOBBY (ahem) and put into a coherent whole that people wanted to play.
The less savory aspect is that EGG tended to forget that he was not the end-all, be-all, of D&D. That he borrowed Chainmail. That he borrowed from Arneson. That he borrowed from other hobbyists (see the prior discussion of the Thief class). Maybe he did this because he thought his work warranted it; after all, there is a great amount skill in taking an unfinished idea (such as Arneson's notes, or the concept of a Thief class) and making them into a finished product. Maybe it's because he thought it was helpful to the mythology and sales of the product (think of Roy Kroc and McDonald's). Maybe it's because he did so very much work and so much writing (early modules, magazine articles, rule sets) that it just all blended in. Who knows?