It is called backside on a board and frontside because they go down the hill sideways.  Assuming that you are regular foot (left foot forward) and you take of regular and spin left, thats backside, spin right, thats frontside.  The pro snowboarders CAN spin both ways just as comfortably, but that doesn't take away from the fact that the spibn is backside or frontside, it just means they are damn good.
As for the unnnatural debate in skiing.  I think that if you are going to spin unnatural in a slopestyle run you should also show that you are just as good or better at spinning the other way.  As for the unnatural debate in big air I honestly don't know.  Jon, dave and I were talking about it and it's hard to figure out what to do in that case.  Example: Cr's 'unnatural' underflip. He does them better his wrong way than his right way, so what do you do there???