I am normally a VERY relaxed person when it comes to food safety but I have gotten poisoning in the US and once it was from fried rice. I would say that leftover rice is FINE but you should take precautions with it. If not cooked properly the 1st time and then left to sit at room temp for too long, it can produce food poisoning.
That said, I'm SUPER relaxed...I don't refrigerate soups, eat raw eggs, very old leftovers and I think all those food restrictions during pregnancy are BS. I've been living this way my entire adult life - 20 years and I've been sick twice. It was worth it. ;-)