I don't think that most of the IWC is in the camp that chants "You can't wrestle" at Cena. I would hope that most realize that practically any trained professional wrestler with over a decade of experience is capable of performing any move that their own physical body proportions allow, even if they look akward when using them(as Cena does when using a move he rarely executes).
I would hope that most of the Cena haters are more focused on his being "stale" or "corny", believing the types of rhetoric that The Rock used to build their match last year. Or they believe stories that degrade his backstage relations.
To claim Cena as being incapable to wrestle effectively in light of some of the matches he has worked seems like a counter-productive argument that you are bound to lose. There is other more relevant fuel available to the haters. But then I could be wrong.