I disagree with you.
So you do not think that this passage is saying that David's faith was counted to him for righteousness?:
"But to him that worketh not, but believeth on him that justifieth the ungodly, his faith is counted for righteousness. Even as David also describeth the blessedness of the man, unto whom God imputeth righteousness without works, Saying, Blessed are they whose iniquities are forgiven, and whose sins are covered" (Ro.4:5-7).
If that is true then why would Paul include him in his discourse which is speaking about salvation by grace apart from works?