No. It's just a huge factor affecting your skin in many, many ways. See the pinned good things thread for info on most of those ways.

Dietary allergic reactions can certainly cause acne.

Bad diet + other factors can cause leaky gut, which most definitely can cause acne (seems to be the main cause for me).

For most people in otherwise perfect health, diet won't cause acne. But most acne sufferers are far from in perfect health.