As been said before you simply don't understand the doctrine of binding and loosing. The Church is the voice of God here on earth on matters of Faith and Morals. God cannot contradict Himself, God cannot endorse what He has forbidden. This doctrine shows God's trust in His Church to carry out His Will on earth as it is in heaven.
I doubt that 'miraculous healing' on the Sabbath was forbidden by the Law of Moses. If it was show us where.