Valve seems to have done a pretty good job dealing with this in their games. Surely there exist more sophisticated anti-cheat mechanisms than "just ban third-party accessories"?
This seems like the kind of thing that is repeated so much because some people want to believe it, and most of the time I bet it's people who haven't played a Valve multiplayer game ever.
I will say, I think the biggest problem contributing to high levels of cheating is the move away from dedicated servers. I actually find that VAC is historically very effective at catching cheaters, but with a necessary lag between detection and bans -- and that lag used to be handled by server admins.