I would be very very uncomfortable with a doctor that said that. I get the "everyone has an epidural" or "that is not real life" because, yes, that is hospital birth for many women. That is the doctor's experience. But someone who thinks that a woman should not move in labor if unmedicated is um, crazy? totally unexperienced with natural birth?
We still haven't clarified with him exactly what he meant. Either he meant walk around the hallways, or walk around the room. Given that there's a squat bar, and birthing ball and birthing stool available, I now have a hard time believing he meant one couldn't walk around the delivery room, and instead meant the hallway. As near as I figure the hospital probably fears that if a laboring women were to walk around the hallways, and suffered a particularly hard contraction, she could take a fall and hurt herself and/or the baby.