Clement of Rome wrote to the church in Corinth around AD 90. This is perhaps the same Clement, companion of Paul, mentioned in Philippians 4:3. Many hold him to be the first bishop / pope in Rome, aka St. Clement I. Clement quotes from the letter to the Hebrews. Origin suggested that Clement was in fact the writer (as transcriber or amanuensis) of Hebrews. Perhaps this letter began as a "word of exhortation" given by Paul at the synagogue (Heb 13:22; cf Acts 13:15) which then became a circular letter for the churches. Other possible authors of Hebrews include Luke, Barnabas, or Apollos. The theology is Pauline, but the transcriber is obviously second-generation (Heb. 2:3-4). At any rate, this early church leader in Rome, is already quoting Hebrews in his letter in AD 90: CHAPTER 36 ALL BLESSINGS ARE GIVEN TO US THROUGH CHRIST This is the way, beloved, in which we find our Savior, even Jesus Christ, the High Priest of all our offerings, the defender and he
Shortly before his death on January 1, 1937, J. Gresham Machen dictated a final telegram to his friend and colleague, Professor John Murray. It was brief:
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Yet Reformers like Luther, Calvin, and others, did not believe in Active Obedience, and they pointed to very powerful texts like 2 Corinthians 5:21, Romans 3:21-26, Romans 4:6-8, and Galatians 2:21, which all frame justification as a matter of the Cross alone and forgiveness, no "active obedience".
Christ's righteousness is seamless, his righteous life and atoning death being inseparable: "with the precious blood of Christ, like that of a lamb without blemish or spot." (1 Pet 1:19). His death would not be perfect and meritorious were he not blameless and unblemished in his (active) life and obedience before the Father. By virtue of our union with Christ are we not united to (and share in) all of Christ and his righteousness.
Yet you have raised a good question as to whether this theological distinction is valid. Will study more.