Bringing us back to the original discussion of whether the concentrations of the constituent elements (calcium and oxalate for that type of stone) matter as much as the properties of the solution.<quoted text>
Kidney stones are fully immersed in liquid (urine) or it could be said that they're formed in liquid by the crystallization of calcium oxalate molecules from supersaturated solution and are as such fully surrounded by the liquid media even if attached to the inner lining of the organ from where they keep moving down the urinary tract as more and even more water that is imbibed by the patient ends up in the kidneys.
With the right pH and ion or other physical exchange, the constituent reagents are whisked away BEFORE they have a chance to precipitate and crystalize. The easiest way to have this happen is simply drink more water. A second way is to imbibe more citrate as it complexes with the calcium (drink more lemonade).
keep in mind there are several types of stones - you need to catch one and send it to a lab to figure which type you have. Calcium oxalate is the most common though.