There are other significant factors beyond the ones you mentioned, such as inflammation due to processed foods, certain oils, and more that are common in industrialized medicine.
Plenty of anecdata of people who stopped eating certain categories of food and certain conditions they had for a long time went away. In my son's case, a severe case of eczema that persisted for years went away in a matter of weeks after we significantly reduced the amount of hydrogenated oil products available to him to eat.
Sure enough, when we would visit my mom's place which had it, and he'd indulge, the symptoms came back. Same thing when we would buy it at home and he's splurge, he'd have the same problems recur. Cutting it out of the diet is the only thing that correlated highly with the absence of the condition. This happened even after a move from one state to another.
One case, not proof, but definitely repeatable in our circumstances. I have heard a LOT of similar stories. Is it proof? No, but it's an amazingly easy thing to try. It's takes an adjustment, but it intuitively makes sense. Processed food of today is something our ancestors wouldn't even recognize as food. It's just not what our bodies were designed to handle. Some can handle it better than others, but such a processed food and artificial sugar-heavy diet can't be called natural or even healthy.