Interesting post! Of course each of these aspects only highlights part of the whole picture. What usually comes to my mind when I hear kidney stones is phosphoric acid, found in many commercial soft drinks. (In certain countries the food label laws are manipulated in such a way that instead of "phosphoric acid" the label just says "food acid". Sounds harmless, right? Check your nearest coke can!)
Phosphoric acid is not really meant to be ingested. The reason they put it in the soda is to counteract the exorbitant sweetness from the insane amount of sugar. But its effect in the body is that it binds minerals such as magnesium and calcium into crystals. So what started out as something beneficial for the body becomes a problem that needs to be gotten rid of... that's right, through the kidneys. If someone thinks they can make up for the loss of calcium due to drinking coke by drinking milk, their plan will backfire in form of more calcium crystals in their kidneys.
But yes, as you mentioned, there are numerous types of stones, being caused by various factors. The two you mentioned I wasn't familiar with, but good to keep in mind the complexity of the picture.