WRONG, as has been pointed out a hundred times. James presided over the council, not Peter. Acts 15:19, AGAIN. Not so infallible, that Church "fact".
Acts 15: "7 And when there had been much disputing, Peter rose up, and said unto them, Men and brethren, ye know how that a good while ago God made choice among us, that the Gentiles by my mouth should hear the word of the gospel, and believe. 8 And God, which knoweth the hearts, bare them witness, giving them the Holy Ghost, even as he did unto us; 9 And put no difference between us and them, purifying their hearts by faith. 10 Now therefore why tempt ye God, to put a yoke upon the neck of the disciples, which neither our fathers nor we were able to bear? 11 But we believe that through the grace of the Lord Jesus Christ we shall be saved, even as they. 12 Then all the multitude kept silence, and gave audience to Barnabas and Paul..."
Peter refereed the dispute between Paul and James, supporting Paul in his position against Judaizing. Peter quieted the crowd and gave Paul the floor. James made the final pronouncement at in the end because he was leader of the party capitulating to Paul.