I think the theory is that the weight of the baby/uterus/placenta/amniotic fluid etc can squish certain veins/arteries nerves etc.

I guess worst case scenario would be restricting blood flow but your body should let you know and you'll turn yourself onto your side.

My chiro also said to think about people that aren't pregnant eg: men who might have a huge beer belly, plenty of them sleep on their back without causing too many problems with blood flow or the like...maybe snoring is a prob