No, not necessarily. Many bins work by simply adding materials to the top while harvesting materials out of the bottom. Turning allows you to add air and, if necessary, moisture to speed up composting. If the opening of the compost bin is too narrow to turn the pile, simply lift the bin up off the compost, place it next to the compost materials and turn them back into the bin. For larger piles, placing a perforated pipe on the ground when starting off can promote both passive aeration and drainage if necessary.
Finally, you can purchase a spiral compost mixer that acts like a giant corkscrew to mix things up in a narrow, stationary bin.