My intuition says that this is qualitatively different. If the agent knows that only one green roomer will be asked the question, then upon waking up in a green room the agent thinks “with 90% probability, there are 18 of me in green rooms and 2 of me in red rooms.” But then, if the agent is asked whether to take the bet, this new information (“I am the unique one being asked”) changes the probability back to 50-50.
My intuition says that this is qualitatively different. If the agent knows that only one green roomer will be asked the question, then upon waking up in a green room the agent thinks “with 90% probability, there are 18 of me in green rooms and 2 of me in red rooms.” But then, if the agent is asked whether to take the bet, this new information (“I am the unique one being asked”) changes the probability back to 50-50.