I think it’s a bit more than that. I think that the idea is that you simplify the problem so that the rubber duck could understand it. Or at least reformulate it in order to communicate it clearly.
It’s the simplification, reformulation or reorganisation that helps to get the breakthrough.
Just thinking out loud isn’t quite the same thing.
Often things like this are intended to be support for something else. Maybe there’s something nearby that’s hinged and can fold down on to it?