According to Harold McGee's On Food and Cooking, rice turns bad pretty fast at room temperature. Here's from "Keeping Rice Safe" (p. 475):
"Cooked rice turns out to be a potential source of food poisoning. Raw rice almost always carries dormant spores of the bacterium Bacillus cereus, which produces powerful gastrointestinal toxins. The spores can tolerate high temperatures, and some survive cooking. If cooked rice is left for a few hours at room temperature, the spores germinate, bacteria multiply and toxins accumulate. Ordinary cooked rice should therefore be served promptly, and leftovers refrigerated or frozen to prevent bacterial growth."
I've always taken that to mean that it's fine to reheat rice as long as it hasn't been standing around for too long before refrigerating the first time around.
"Cooked rice turns out to be a potential source of food poisoning. Raw rice almost always carries dormant spores of the bacterium Bacillus cereus, which produces powerful gastrointestinal toxins. The spores can tolerate high temperatures, and some survive cooking. If cooked rice is left for a few hours at room temperature, the spores germinate, bacteria multiply and toxins accumulate. Ordinary cooked rice should therefore be served promptly, and leftovers refrigerated or frozen to prevent bacterial growth."
I've always taken that to mean that it's fine to reheat rice as long as it hasn't been standing around for too long before refrigerating the first time around.