No, I think you are thinking about the current crop of military fast jets. They rely on computer control (fly by wire) as they are designed to be unstable so that they respond faster.
Snapping into a 9G turn is not something we require our passenger a/c to do. There would be a few G&T's spilt, not to mention the trifling issue of the airframe being ripped apart!
Airbus use fly by wire for other reasons other than purely for stability control. Basically because we pilots like to do things the engineers would rather we didn't and the FBW helps stop that. (i.e flying into the ground and taking no corrective action. If the system can detect it, then it'll do something even if you don't.)