Paul is saying, "If you go to man's law in charging your brother, you have already lost! It does not matter how the judge decides it; as far as God is concerned, you have lost the case!"
Paul's instructions are clear. In a case involving brothers, a Christian had better be prepared to "lose," as an act of faith, out of respect for Christ, the Head of this church. By faith, we know that He will judge the situation. Does He have enough wisdom to do that—and power to carry out His judgments? Do we have enough faith to allow Him to do it?
Is there a legal basis for this? Absolutely—He owns us! We are His slaves! He purchased every single one of us with His blood! He has legal right to judge between brothers. We are to submit to the authority of Christ by faith and allow Him to judge if no judgment can be reached within the church. If a judgment is reached within the church, but the church has judged wrongly, then the brothers must be willing to accept it with the knowledge that they can, by faith, appeal to a higher court, and that Christ will vindicate the righteous. It may not happen right away, but if we pray for that in faith, then we can patiently wait for it. He will do it!