No, he is not saying that.
All true believers do have good works and righteous acts.
David meant first of all that the imputed righteousness of Christ was the only grounds of a sinner's acceptance before God. Moreover, David also meant that the good works and righteous acts of the believer do not stem from a self-righteousness, but the impartation of God's righteousness. My righteousnesses are as filthy rags, and the only hope I have is the righteousness of Christ. This is the only righteousness I feel safe mentioning to God, and this is the only righteousness I feel safe mentioning to men. I have made mention of Thy righteousness, even Thine only.