Why would any of these things cure diarrhea? Won't it just pass given time?
Starchy foods are binding. Either fat or fiber foods are laxative. So Rosie's suggestion made a lot of sense to add burger to encourage the dog to eat the rice while limiting the fat as he doesn't need anything laxative right now.
Diarrhea can be life-threatening due to electrolyte loss; it's one of the most common causes of death in infants worldwide.
I don't know if it's as critical in dogs, but even if not, living with an incontinent dog isn't exactly something one would be patient about.