Well, generally, the person who states a link exists is usually the one who should prove it. It is incredibly difficult to prove a lack of difference.
However, I will refine my statement. There is no evidence in the medical literature that there is a link between diet and acne. There are few studies, but the ones that have been done don't prove an effect. I did a quick search and limited it to pubmed articles available for free.
Here is a review article:
Here is another article. Even though this study is flawed and very small, it shows no link between diet and acne (but it does show a link between weight and acne):
Considering insulin's role in acne is interesting, but it is only a hypothesis, and not a very well supported one. The authors of one article cite polycystic ovary syndrome as an example of a disease with high insulin and acne. However, there are other diseases with high insulin which are not associated with acne. I seriously doubt insulin elevation causes acne, it is probably something else. PCOS patients for example are usually obese.
I respect your enthusiasm and intellect, but you are on the wrong track with this article. Please be careful when you give people medical advice unless you are a trained and licensed physician.