Can uncooked rice be stored in the freezer or refrigerator?
First, in general freezing is possibly the best method for storing grains long-term if you're not going to use them up within a few months.  So it's never a bad idea to freeze dried wheat, rice, buckwheat, etc. if you have the space.  Certain grains, like wheat germ, contain oils that oxidize quickly and have to be stored cold or they go rancid in a few weeks.
This is also the issue with Carolina Gold Rice, according to Anson Mills:

With regard to your fresh cold milled to order hand pound emulation Carolina Gold Rice... because we choose to emulate how rice was prepared from scratch paddy rice a la minute for cookery before the industrial revolution, we hull/mill so that we just nick the outer bran of each kernel leaving the inner bran layer and germ intact... this form can oxidize and/or spoil stored at room temperature even though we vac pack on CO2 envelope at -10 F. to protect this rice for shipment at ambient temperatures for about 2 weeks only. We mill this way for flavor..

So, the rice bran is still attached to the rice, and contains easily oxidized oils, which means it will lose flavor or even develop off flavors within a few weeks at room temperature.  Tip: freeze it in the quantities you'd usually cook it in, makes it easier to take some out for use.