Exactly - Rumsfeld is just a bureaucrat - he enacts whatever policy Bush & Cheney & Rice tell him to enact.
Dubyah is the one who flinched, and decided not to visit Armageddon upon the Muslims, and the result is that the Muslims were emboldened and realized that they could "win" this thing at the ballot box, just like the Russkies & Chicoms & North Koreans did in the Korean "War" [really the Korean "Nation-Building Exercise"], and just like the Russkies & Chicoms & North Vietnamese did in the Vietnam "War" [really the Vietnamese "Nation-Building Exercise"].
The irony of all of this is that Dubyah forcefully renounced the whole idea of nation-building exercises during the 2000 debates with Al Gore, and if he had only stuck to those promises, then everything would be hunky-dory today.
It is Rumsfeld's doctrine of throwing unnecessarily limited resources at Iraq that has gotten us where we are. You win wars by using overwhelming force.