Short answer. Yes.
Raw rice carries bacteria, which can survive during the cooking process (although unlikely) and can produce toxins in the body.
It all comes down to food storage. Once you have eaten, put your leftover rice in the fridge to chill. The longer rice is left at room temperature, the more time the bacteria (if any) have to thrive.
The NHS recommends putting cooked rice in the fridge within 1 hour and binning cooked rice after 24 hours.
Many Asian fried rice dishes rely on cooked rice to start with. They generally boil there rice and then chill 1-2 hours after in preparation for frying it. So do not worry yourself!