It's true that you could get food poisoning from eating reheated rice.
But it's not actually the reheating that's the problem – it's the way the rice has been stored before reheating. Uncooked rice can contain spores of Bacillus cereus, bacteria that can cause food poisoning.
When the rice is cooked, the spores can survive. Then, if the rice is left standing at room temperature, the spores will germinate into bacteria. These bacteria will multiply and may produce toxins (poisons) that cause vomiting or diarrhea.
Reheating the rice won't get rid of these toxins.
So, the longer cooked rice is left at room temperature, the more likely it is that bacteria, or the toxins they produce, could stop the rice being safe to eat. It's best to serve rice when it has just been cooked.
If that isn't possible, cool the rice as quickly as possible (ideally within one hour) and keep it in the fridge for no more than one day until reheating. You can of course freeze cooked rice, just be sure to follow the previously mentioned instructions of cooling it quickly.
Remember that when you reheat any food, you should always check that it's piping hot all the way through, and avoid reheating more than once.