As with all food, it's not the reheating that is the problem, it's the cooling down which is. The reason for this is that you generally reheat stuff and eat it fairly quickly afterwards, so there's not a great deal of time for any bacteria to multiply etc, whereas left over food can be hanging around for a good while at nice germ breeding temperatures if it's not cooled quickly enough.
However, saying that, I think the recommended times are something like to fridge temps within 90 mins... so unless the rice has been hanging around at room temperature for ages there really shouldn't be a problem.
Edit: am now trying to remember exactly what t'other half told me, but I don't think the bacteria which is the problem with rice is actually killed by the temperatures used in cooking, which is why cooling the rice quickly is important to stop it growing. Also, it's not the bacteria directly which is the problem, when it is cooled it forms a protective coating around it, which gets thrown off when reheated and it's this coating which is the horrible bit... or something like that.
Also, you should never really put hot/warm stuff in the fridge as it raises the fridge temperature... rice would probably be okay, but anything much bigger would warm the fridge up a good few degrees while it cools...