You mean begrudgingly being forced to rename hobbits, ents, and balrogs, as halflings, treants, and balors, and claiming forever thereafter that Tolkien wasn't an influence.It would be interesting to see how the game would have developed if Gygax had been a Tolkien fan, rather than begrudgingly adding in Tolkien influences.
D&D was definitely inspired by Tolkien. Mountain dwarves, high and wood elves, halflings, treants, balors, mithril/al, rangers, orcs, nazgul/wraiths, Moria (the dungeon)... he can claim he wasn't inspired by Tolkien, but that's clearly not true. I agree that after Tolkien forced him to change the game, though, he was definitely not a fan. And, it seems, would never again admit to having been one, or being influenced by it.
That D&D was inspired by Tolkien (amongst other things of course) is clearly a post-legal fiction. The truth was right there in the pages of D&D in black-and-white.
(In fairness, we're talking about TSR, not just Gygax; he didn't work in isolation).