Statistics are the core of an RPG, it's what makes your character truly unique to you. As you play your character it will progress and grow in a manner of your choosing. Bethesda have already opted to drop a lot of this with Skyrim.
Removing character progression takes away a lot of the RPG aspect and makes it an action game, where your character development is essentially entirely story-driven. The only thing that would separate your character from other people's characters is how it looks and which perks you chose, if that's how some people would define an RPG then Modern Warfare 3 is an RPG.
No, Modern Warfare is not an RPG because you have no choice. For me, choice is what makes up the core of an RPG.
Diablo has a lot of stats but I don't consider it a true RPG because there's no real dialogue or choices. Games like Mass Effect and Deus Ex are more RPG than Diablo even though they are shooters as well. If it was just stats then stuff like NBA 2k12's My Player mode would be RPGs. Similarly, Fallout New Vegas is more of an RPG than Fallout 3 or any Elder Scrolls game (at least since Morrowind, didn't play before it) precisely because of things like choice and better fleshed out dialogue.