St. James, the Bishop of Jerusalem spoke up to affirm the declaration made by St. Peter because the disagreement had arisen within his diocese (Judea). Look to the preceding versus to your citation for the entire truth:
"After much discussion, Peter got up and addressed them: “Brothers, you know that some time ago God made a choice among you that the Gentiles might hear from my lips the message of the gospel and believe. God, who knows the heart, showed that he accepted them by giving the Holy Spirit to them, just as he did to us. He did not discriminate between us and them, for he purified their hearts by faith. Now then, why do you try to test God by putting on the necks of Gentiles a yoke that neither we nor our ancestors have been able to bear? No! We believe it is through the grace of our Lord Jesus that we are saved, just as they are.” - Acts 15:7-11
Of course Peter was the one to speak about the Jews. He was the apostle to the Jews. It was still James who was the obvious leader of that meeting.
Rome: No! We believe it is through the sacrement of baptism that we are saved!