OK, you guys convinced me. The gist is that since you are in compliance with the rules in moving the branch you are not subject to 1-2 under Exception 1. IOW, if you move the branch so it no longer obstructs you but still obstructs your opponent you are fine. Your opponent has the option of leaving the branch where you move it or moving it back to its original position. I inferred that the key is that you did not disadvantage your opponent since the branch was already interfering with the ball. So when you moved the branch so that it still interfered with his ball you were not disadvantaging him and you were operating in accordance with a specific rule.
They did not address the issue of what your obligation is in a stroke play competition in regard to protecting the field. But they did say that if the player in the bunker asked the other player to move the branch he would be subject to DQ. I would infer from this that I might have an obligation to move the branch so that it does not interfered with me while still interfering with the fellow competitor in order to protect the field.