You're close to right. The "vegan honeymoon" - as an example - is an example of why many people will feel better cutting out bad foods, however carbohydrates and sugars are some of the largest inflammatory factors from my understanding, so cutting that out will help. Following vegan or omnivore doesn't mean eating a balanced (carbs, fat, protein) diet nor anti-inflammatory, doesn't mean eating a diet specifically that is healthy for your body either - doesn't remove foods you may individually be sensitive to.