Yeah, the argument "If you don't count CI or CO correctly, CICO doesn't work, therefore CICO is debunked" is pretty silly. As an accounting mechanism, it's basic physics. If CI<CO, you will lose weight -- you might not find it easy, you might not thrive, you might not even survive, but the universe itself will make sure that you lose weight.
I don't think that's really what the authors intended to tangle with, though. I agree it came off that way, but maybe we are all just a bit touchy from 1001 fad diet pitches that all begin by trashing CICO in exactly the way the authors did, because if you get good at CICO you are in a position to actually evaluate whether or not the fad diet is any good, which is a big problem for most fad diets.
Here's why I have less of an issue with CICO trashing in the context of this article: the authors are trying to figure out explanatory mechanisms for the obesity epidemic. They are spot on to point out that CICO says nothing about the feedback mechanisms that control CI and CO, and that figuring out those mechanisms is key to figuring out the obesity epidemic. CICO is correct as far as it goes, but it doesn't go where the authors are going.