Scott, those local churches had to obey the council because the Apostles were the ones writing the letters that became Scripture. The Apostles laid the foundation of Church doctrine. That foundation has been laid once and need not be laid again.
A church is autonomous in that it is under the authority of Jesus Christ Himself who appoints elders within that church to be representatives of his authority in that church. I'm not the only one who believes in this...many Baptist churches do. This statement below is taken from my church's website:
THE CHURCH
We believe that the New Testament local church is a company of immersed believers voluntarily associated together for: the ministry of the Word, mutual helpfulness and edification, observances of the ordinances, and fulfillment of the Great Commission (making disciples, baptizing, and teaching unto the ends of the earth). We believe the church is to be sovereign and under no higher ecclesiastical authority. We believe that Christians are to live in newness of life by being separated unto God from the carnal indulgences of the world.
(Matt 28:18-20; Acts 2:42, 8:36-39; Heb 10:25)
Also, since a historical event can be precedent how come many people on here don't believe we can use musical instruments in worship when historically they were used? (Rhetorical question, I don't want to take the thread off topic)