The problem is with cooked rice that hasn't been cooled off properly (or not kept hot enough). The heat-resistant spores of the Bacillus Cereus will then develop and the bacteria will proliferate and produce a heat-resistant toxin, which can hurt you even after reheating the leftover rice.
You need to keep your rice cold (<7 °C) or hot (>63 °C) enough for the spores not to develop. Letting your rice cool off naturally in a pot is also leaving it at the wrong temperatures for a longer time than if you rapidly cool it off.