If you knit on one side and purl on the other, stranding is not a problem. When you knit, the yarn is at the back, so it gets stranded there. When you purl the yarn is across the front and gets stranded there. This way the yarn is always stranded along the same side.
If you knit every row, and strand across the back, then when you turn your work that becomes the front and you have to strand across the back again. Understand?
Is there a place I can look at a picture of these? You've gotten me curious now.
Actually, I found a pattern. Looking at the picture, the stripes are not stranded per se on the inside. It looks like intarsia to me.
Anyone else--if you can explain it better, please do.