The main reason for the belief that consciousness is being produced by the brain is that if you destroy a portion of the brain, the consciousness of the individual is diminished. We can even point to specific deficits that occur if we destroy specific portions of the brain.
But this is does not imply that consciousness is being produced by the brain. If a television is broadcasting a news program, and you destroy the television so you can no longer see or hear the news anchor, this does not imply that the news anchor was inside the television and is now dead.
Rather, the television is a receiver of a signal that then allows you to interact with the contents of that signal. Likewise the brain may be a receiver of consciousness, something through consciousness can interact or express itself. If you take away the receiver, the signal, and the origin of the signal, remain intact.
An artist uses paintbrushes to produce paintings. If you take away the paintbrush and give him crayons, the quality of the art produced may be different, but you have not destroyed or limited the artist himself. Take away all the artist's coloring tools, and the artist remains, ready to take up any other instruments that may be available