You can see it more clearly in @Kirk’s work. Also try take a look at this paper, which was referenced early on.
You might think it is obvious they failed, but trust me, it is not obvious to most people. This is usually what they are referring to when they talk about “information”. I agree with you, that they have not made their case. However they certainly are trying. If not trying, it is because they are claiming such total victory that there is no more reason to do research on this (yes, that can be the rhetoric).