Well, here's the thing: in a sense, I think this is true. It's just not at all the sense in which the people saying it mean it...if that makes sense.
Let me see if I can explain:
A lot of old-school players remember when tabletop games were THE thing. For one brief, shining instant, our hobby was relevant, popular, and trendy. Heck, it was even edgy and controversial and (dare I say it?) ...cool.
I think a lot of older players harbor the hope that tabletop games will regain their glory and their position at the top of the heap, and that's simply never going to happen.
The truth is that MMORPGs have ruined D&D and other tabletop games in one very specific sense: they've made them archaic and (to a majority of would-be gamers) obsolete. Johnny Future Gamer is faced with a choice: he can memorize a stack of rulebooks, get together multiple friends, convince THEM to memorize those rulebooks, and then find three-to-six hour chunks of time where they can all get together and play.
Or, he can click on an icon on his desktop and be playing within five minutes or so of installing the game.
The convenience factor of MMORPGs is something tabletop RPGs just can't match--and, for a lot of gamers, that convenience factor means that MMORPGs are simply the superior option. That's true no matter how much those of us who love tabletop gaming wish it weren't so.
The busy career-focused young professional who doesn't have much free time, but still wants to game? The MMORPG meets his or her needs better.
The stay-at-home parent who would like to game, but has to squeeze it in in 30 minute chunks while the kids are napping? The MMORPG suits his or her needs better.
The younger gamer who really doesn't want to spend a lot of time poring over rules? The MMORPG meets his or her needs better.
Games like WoW aren't going to kill D&D or tabletop gaming in general. They are going to do to them what tabletop RPGs did to tabletop wargames: relegate them to a corner as a small, niche hobby which is relatively insignificant in the big picture.
In fact, they've done that already.
Now: that being said, I think that the people who reflexively say, "WoW has had no influence on D&D!" are kidding themselves. Yes, WoW has had an influence on D&D. Of COURSE WoW has had an influence on D&D. The designers of D&D, by and large, aren't idiots. They know WoW offers a style of play that is extremely popular and attracts a MASSIVELY larger audience than D&D, and they'd like to cut off a piece of that pie for themselves.
So, no: the suspiciously similar elements in recent editions of D&D aren't just coincidence; they're a reasonable and reasoned attempt by a business to appeal to a larger audience...and there's nothing wrong with that.
Heck, there's also nothing new about the denialism. Back in the 1970's, it was "D&D ripped off Tolkien!" "No it didn't! There's almost no Tolkien influence in D&D!"
The more things change...