See e.g. http://www.scientificamerican.com/article/why-paleo-diet-hal... or dozens of subsequent pieces.
The better way to phrase this is to avoid trying to claim unique merit: “This diet works for me. Maybe it will work for you.” That keeps the truthful part but drops the magical claims about why everyone else's choices aren't as valid.
For instance, this article:
http://www.ncbi.nlm.nih.gov/pmc/articles/PMC1856434/
which I found linked from a nutritionist promoting AIP, only goes as far as
However, in several autoimmune conditions it appears that increased permeability is a constant and early feature of the disease process. Furthermore, it is becoming increasingly apparent that in some conditions increased permeability is critical to the development of disease as if it is abrogated the disease does not develop.
Note all the equivocation in the science there.
Edit: Actually linking one might be difficult, but for such a categorical statement, you should be able to cite a recent textbook, not just a few articles.
Counting calories is an extremely simplistic world view, and while it's very comforting to have a simple rule to follow, I believe it's a very bad idea to not care what you put in your body, as opposed to just how much of it.