EY's "I don't know." is an interesting way of treating open-ended scenarios. Does it apply to "pick Red or Green"? This isn't strictly what you linked to, I suppose, so that may not be relevant to what you were trying to say.

And they have to do something, because even refusing to circle an answer is a course of action. It's just that in this case we don't have any reason to be very confident in any specific choice.

So, when asking for an action, wouldn't "do nothing" be included in the choices? In other words, the three options are "Pick Red", "Pick Green", "Do nothing", and Alice and Bob choose randomly from those three?