This study by Loren Cordain, the antropoligist founder of the paleo-diet, is flawed in several ways. Isolated tribes lead completely different lives from Westernerns. They also often share very little genetic material with us. E.g two neighbouring African tribes can be genetically more separated than all white people in the whole world.
Regarding acne and diet, here are two quotes from two meta studies:
"We did not realize how daunting it would be to write an article dedicated to making sense of the relationship of acne to foods. It turns out that there are no meta-analyses, randomized controlled clinical studies, or well-designed scientific trials that follow evidence-based guidelines for providing solid proof in dealing with this issue."
https://www.ncbi.nlm.nih.gov/pmc/articles/PMC2836431/
"Despite the inundation of epidemiologic studies, mostly of unsatisfactory quality, and the abundance of beliefs and perceptions among acne patients about the role of diet in the pathogenesis of acne, there is a paucity of reliable information. In the few studies that have been undertaken, no specific foods (including fatty foods and chocolate) have been identified as causative factors. Yet, the question of whether common perceptions and beliefs prove to be fact or misconception is more than an academic issue. It is of importance due to the practical implications of these beliefs for acne management.
Alas, after reviewing the relevant published data, we can conclude that insufficient serious effort has been invested in investigating these questions, which are prevalent and consistent across different cultures. At present, we are bereft of reliable answers based on scientific evidence. We hope that the day when we will be able to knowledgeably advise our acne patients on the role of nutrition in relation to acne etiology is not too far away."
http://centrespringmd.com/wp-content/uploads/2013/05/The-Rol...
Both mention Cordain's study and explains why it is no good. If you believe diet is causing acne, you might as well believe in homeopathy and healing too. All the anecdata in the world cannot change that.
If you think X (eating "bad" food) causes Y (acne), then observing (not X)and(not Y) doesn't prove anything because there is no PREDICTION involved. However, there is an obvious way to try and test the causality; DO X and observe Y. Eat as much pizza and chocolate and drink as much milk and soda you want. If you after t days have a face full of acne then CONGRATULATIONS! You have done something thousands of dermatologists have been unable to - namely demonstrated a causative link between diet and acne. It would truly be a huge breakthrough and you would have revolutionized the science of dermatology.
I find it very odd that, despite all the anecdotes, not a single person has conducted any such experiment.