Bring first 5 ingredients to a boil in a Dutch oven over medium-high heat. Cover, reduce heat to low, and simmer, stirring occasionally, 1 1/2 hours or until meat is tender.
Stir in rice; cover and cook over low heat 20 to 25 minutes or until rice is done. (Do not stir.) Fluff rice with a fork, and serve.
Note: Pork backbones are also sold as "country-style ribs."